Thread: ODE finding constants...
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Old November 4th, 2009, 03:17 AM
HallsofIvy HallsofIvy is offline
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Originally Posted by matlabnoob View Post
another problem i worked half way on and stuck on

ODE is dx/dt = x^(3/4)

i need to find values for constans a > 0 and b or which x(t) = (at)^b is a solution of the ODE or t>0. Is this function also a solution for t<0?

ok, so here goes my crazy method in doing this..



x'(t) = ba(at)^(b-1)

put this into the ODE:

ba(at)^(b-1) = ((at)^b)^3/4

now what?.. no initial conditions are given. how do they expect us to find a and b =S and..... determine t? =| that looks crazy.. how you obtain a,b,t from that equation


thank you
ba(at)^{b-1}= ba(a^{b-1})t^{b-1}= ba^b t^{b-1} and ((at)^b)^{3/4}= (at)^{3b/4}= a^{3b/4}t^{3b/4}.

In order that those be equal for all t, we must have ba^b= a^{3b/4} and b- 1= 3b/4.

That last equation gives 4b- 4= 3b so b= 4. With that, the first equation becomes 4a^4= a^3 so either a= 0 or a= 1/4.
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