Math Help Forum - Differential Equations http://www.mathhelpforum.com/math-help en Sat, 21 Nov 2009 01:56:46 GMT vBulletin 60 http://www.mathhelpforum.com/math-help/images/MHF/misc/rss.jpg Math Help Forum - Differential Equations http://www.mathhelpforum.com/math-help żunsolved problems in differential equations? http://www.mathhelpforum.com/math-help/differential-equations/115817-unsolved-problems-differential-equations.html Sat, 21 Nov 2009 01:12:57 GMT Hi, I would like to talk with you about the modern lines of investigation about differential equations ( ode,pde...) , which are the most interesting unsolved questions, ecuations to solve, general tools for solving differential equations ....(Smile) I know we have learned a lot, but still... Hi, I would like to talk with you about the modern lines of investigation about differential equations ( ode,pde...) , which are the most interesting unsolved questions, ecuations to solve, general tools for solving differential equations ....(Smile)

I know we have learned a lot, but still there is a lot of work to do . ]]> Differential Equations arnoldpredator http://www.mathhelpforum.com/math-help/differential-equations/115817-unsolved-problems-differential-equations.html Zombie PDE model http://www.mathhelpforum.com/math-help/differential-equations/115814-zombie-pde-model.html Sat, 21 Nov 2009 00:16:32 GMT Hey guys,

I'm currently taking a Partial Differential Equations class, and for one assignment we have to come up with a model for a theoretical zombie outbreak. Well anyways, this is what I have gathered thus far:

- I am defining my u(r,z,t) to be the population density of humans, where r=radius, z=zombies, and t=time.
- There will be a continuous flow in and out of humans out of the boundary.
- I am letting my boundary be a circular region, suppose a 35 meter radius.
- The population density of both zombies and humans is dependent on the radius, r, of the region. For example if you have 100 zombies in a particular radius with 50 humans, if you increase the radius then the population density decreases.

I think I may have my boundary condition where Du/Dr(35,z,t)= flux, since the normal derivative will always be the radius.

My Initial condition is u(r,z,0)= u0

Now, the PDE is where I am having trouble, I can't figure out what Du/Dt is (the rate of change of human population density with respect to time).I tried modeling it similar to the heat equation, but that doesn't work since I only have one spatial dimension in r, and no theta. As r changes as does the total density (zombies and humans) and therefore human density. ]]> Differential Equations Lionheart814 http://www.mathhelpforum.com/math-help/differential-equations/115814-zombie-pde-model.html laplacian http://www.mathhelpforum.com/math-help/differential-equations/115611-laplacian.html Thu, 19 Nov 2009 19:10:36 GMT I need to solve: \nabla ^2 T = 0 with T=T(r) and r=a/T=T1 and r=b/T=T2 Can anyone offer advice as to the solution? I need to solve:
\nabla ^2 T = 0 with T=T(r) and r=a/T=T1 and r=b/T=T2

Can anyone offer advice as to the solution? ]]> Differential Equations bigdoggy http://www.mathhelpforum.com/math-help/differential-equations/115611-laplacian.html homogeneous solution?? http://www.mathhelpforum.com/math-help/differential-equations/115587-homogeneous-solution.html Thu, 19 Nov 2009 17:02:15 GMT Hi guys I am really stuck on this differential equation can anyone help? dy/dt = (t^2 + y^2) / (3ty) condition - y=1 and t=2 Thank you in advance (Wink) Hi guys I am really stuck on this differential equation can anyone help?

dy/dt = (t^2 + y^2) / (3ty)

condition - y=1 and t=2

Thank you in advance (Wink) ]]> Differential Equations Charlieengineer84 http://www.mathhelpforum.com/math-help/differential-equations/115587-homogeneous-solution.html Determing points of singularity http://www.mathhelpforum.com/math-help/differential-equations/115427-determing-points-singularity.html Wed, 18 Nov 2009 22:24:13 GMT I do not know how to determine if x=0 is a regular or irregular singular point for x^{2}y'' + 2(e^{x}-1)y' + (e^{-x}cos(x))y=0. How do I determine if 2\frac{e^{x}-1}{x} and e^{-x}cos(x) are analytic? ]]> Differential Equations Pinkk http://www.mathhelpforum.com/math-help/differential-equations/115427-determing-points-singularity.html 2nd order PDE - help needed http://www.mathhelpforum.com/math-help/differential-equations/115417-2nd-order-pde-help-needed.html Wed, 18 Nov 2009 21:39:27 GMT H''(n) + (1/2)n*H'(n) = 0.

Boundary conditions: H(0) = 1, H(inf) = 0.

I really don't know where to start ... any help will be greatly appreciated. ]]> Differential Equations Baluba http://www.mathhelpforum.com/math-help/differential-equations/115417-2nd-order-pde-help-needed.html convolution integral http://www.mathhelpforum.com/math-help/differential-equations/115313-convolution-integral.html Wed, 18 Nov 2009 05:34:19 GMT Establish the distributive property of the convolution integral. f*(g1+g2)=f*g1+f*g2 (distributive law) Thanks. Establish the distributive property of the convolution integral.

f*(g1+g2)=f*g1+f*g2 (distributive law)

Thanks. ]]> Differential Equations elmo http://www.mathhelpforum.com/math-help/differential-equations/115313-convolution-integral.html Help with a seperable variable? I think? http://www.mathhelpforum.com/math-help/differential-equations/115210-help-seperable-variable-i-think.html Tue, 17 Nov 2009 23:59:31 GMT Hello all. I'm trying to solve an equation of the form:

\frac{dx}{dy}=\frac{x^2 + y^2}{3xy}

I'm thinking that I can use seperable variable on it, but am stumped as to how to get it into that form. A colleague has suggested using substitution, but sadly my hours of trawling through textbooks/internet has left me feeling frustrated and uncertain. Any pointers where to look would be greatly appreciated.

Thanks ]]> Differential Equations mrlibertine http://www.mathhelpforum.com/math-help/differential-equations/115210-help-seperable-variable-i-think.html 2nd Order PDE hyperbolic http://www.mathhelpforum.com/math-help/differential-equations/115157-2nd-order-pde-hyperbolic.html Tue, 17 Nov 2009 16:13:24 GMT Hi, I have to find the general solution to this second order pde.

x^2Z_{xx} - y^2Z_{yy} = 0 Where x and y not equal to 0.

I have found characteristics to be n=xy and v=y/x and I have used these to change the variables to get

Z_{vn} = 1/(2n) Z_v

And now i'm stuck, for some reason I just dont know how to solve this with the first order partial derivative on the RHS.

Please help.
Thanks Katy :) ]]> Differential Equations harkapobi http://www.mathhelpforum.com/math-help/differential-equations/115157-2nd-order-pde-hyperbolic.html <![CDATA[Simple "For what value of r does it satisfy..."]]> http://www.mathhelpforum.com/math-help/differential-equations/115141-simple-what-value-r-does-satisfy.html Tue, 17 Nov 2009 13:59:50 GMT We sort of blew through this chapter, so I'm not sure how to do this:

For what values of r does the function y=e^{rx} satisfy the differential equation 6y'' + 11y' - 2y = 0?

Would I literally just derive it and solve for r? Seems really messy. ]]> Differential Equations Open that Hampster! http://www.mathhelpforum.com/math-help/differential-equations/115141-simple-what-value-r-does-satisfy.html Solution to a PDE http://www.mathhelpforum.com/math-help/differential-equations/115107-solution-pde.html Tue, 17 Nov 2009 08:42:22 GMT Hi guys, Suppose we have the following PDE for \psi (x,y,z): u(z) \frac{\partial \psi}{\partial x} = \frac{\partial}{\partial y}(K_y \frac{\partial \psi}{\partial y}) + \frac{\partial}{\partial z}(K_z \frac{\partial \psi}{\partial z}) + S Where: S = Q \delta (x) \delta (y - y_s) \delta... Hi guys,

Suppose we have the following PDE for \psi (x,y,z):

u(z) \frac{\partial \psi}{\partial x} = \frac{\partial}{\partial y}(K_y \frac{\partial \psi}{\partial y}) + \frac{\partial}{\partial z}(K_z \frac{\partial \psi}{\partial z}) + S

Where:
S = Q \delta (x) \delta (y - y_s) \delta (z - z_s)
u(z) = a z^p
K_z (z) = b z^n
K_y = 0.5 u(z) \frac {d (\sigma _y ^2 )}{dx}


I have found in the literature a solution for this PDE:

\psi (x,y,z) = \frac {Q}{\sqrt{2 \pi} \sigma _y} \cdot exp[- \frac {(y - y_s)^2}{2 \sigma _y ^2}] \cdot \frac{(z z_s)^{(1-n)/2}}{b \alpha x} \cdot exp[- \frac {a(z^2 + z_s ^2)}{b \alpha ^2 x}] \cdot I_{- \nu} [\frac {2 a (z z_s)^{\alpha / 2}}{b \alpha ^2 x}]

Where:
\alpha = 2 + p - n
\nu = (1-n)/ \alpha

and I_{- \nu} is the modified Bessel function of order - \nu.


I have a reason to doubt this soultion, which comes from physical limitations. It seems to me that the arguments of the last exponent and the Bessel function has different units, providing that \alpha \not= 1. can anybody verify if this solution works for n = 0, or if it works at all? ]]> Differential Equations Marril http://www.mathhelpforum.com/math-help/differential-equations/115107-solution-pde.html IVP With Laplace http://www.mathhelpforum.com/math-help/differential-equations/115092-ivp-laplace.html Tue, 17 Nov 2009 06:17:07 GMT (t-2); y(0) = 0 ; y'(0) = 0 ..... Do laplace of both sides and end up with... e^-2s * inv laplace [ 1 / (s^2 +4s +29) ] I tried to comp the square, but it didnt seem to work out quite like i needed... 1 / ( (s+2)^2 + 25) it looks nice bec 25 is a square too, but i...]]> y"+4y'+29y = <delta>(t-2); y(0) = 0 ; y'(0) = 0
.....
Do laplace of both sides and end up with...
e^-2s * inv laplace [ 1 / (s^2 +4s +29) ]
I tried to comp the square, but it didnt seem to work out quite like i needed...

1 / ( (s+2)^2 + 25)

it looks nice bec 25 is a square too, but i dont know what to do if i did that... i could +4 -4 to top, but i still feel like i am stuck? any help (Hi) ]]> Differential Equations Smac http://www.mathhelpforum.com/math-help/differential-equations/115092-ivp-laplace.html diffusion equation with initial condition http://www.mathhelpforum.com/math-help/differential-equations/115087-diffusion-equation-initial-condition.html Tue, 17 Nov 2009 05:36:03 GMT du/dt = k*d^2u/dx^2 with initial condition u(x,0) = x^5 homework problem that hasnt been covered in class yet.. any help please? du/dt = k*d^2u/dx^2 with initial condition u(x,0) = x^5

homework problem that hasnt been covered in class yet.. any help please? ]]> Differential Equations wrathofkon http://www.mathhelpforum.com/math-help/differential-equations/115087-diffusion-equation-initial-condition.html separable equation http://www.mathhelpforum.com/math-help/differential-equations/115035-separable-equation.html Tue, 17 Nov 2009 03:01:28 GMT could someone please help me with this one? my answer doesn't match the one in the book so i know i'm doing something wrong but i'm not sure where.

\frac{dy}{dx}=\sqrt{y}cos^2\sqrt{y} ]]> Differential Equations yaykittyeee http://www.mathhelpforum.com/math-help/differential-equations/115035-separable-equation.html Partial differentialtion http://www.mathhelpforum.com/math-help/differential-equations/114892-partial-differentialtion.html Mon, 16 Nov 2009 10:38:36 GMT I hiave a question that I am having a bit of a problem with, i wonder if anyone could help. I don't know where to go with it after the point i have reached already. The question is:

The coefficient of rigidity n of a wire of length L, and uniform diameter d is given by

n=(alpha)L/d^4

Where (alpha) is a constant. If errors of up to + or - 0.1% & + or - 0.5% are possible in measuring L & d respectively, determine the maximum percentage error in the calculated value of n, assuming (alpha) is known exactly.

I have sdone the following so far.

|(delta)L/L x 100| less than or equal to + or - 0.1, |(delta) d/d x 100| less than or equal to + or - 0.5

n = (alpha)L/d^4 => n(sub)l = (alpha)/d^4, n subd = -4 (alpha) L / d^5

(delta)n approx. = n subL + n subd x (delta)d

=> (delta)n approx. = (alpha)/ d^4 (delta)L - 4(alpha)L/d^5 x (delta)d

=> (delta)n/n approx. = d^4/(alpha)L [(alpha)/d^4 x (delta)L - 4(alpha)L/d^5 x (delta)d] ]]> Differential Equations scott.b89 http://www.mathhelpforum.com/math-help/differential-equations/114892-partial-differentialtion.html