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CaptainBlack · #2 November 26th, 2008, 11:07 PM

Quote:

Originally Posted by Rapha

Hello everyone!

I need to solve a IVP, for example

$\dot{x} = x + 2\dot{y} + y$

$\dot{y} = y - 2\dot{x} + 5x$

x(0) = 0.995
y(0) = 0

(I actually don't know if there is a solution...)

But how to solve it by using ode45? $\dot{x}$ depends on $\dot{y}$ and y ...

By the way,
I know how to solve

$\dot{v}(t) = 10 - 5/2*v^2(t), t\in [0, 10]$

v0 = v(0) = 0

for example:

[ t , v ] = ode45 (@( t , v ) 10-5v^2/2 , [0, 10], v0 ) ;

----
How to solve the IVP with 2 equations?

Best regards,
Rapha

Eliminate the $\dot{y}$ term in the first equation by substituting from the second, and $\dot{x}$ for the second by substituting from the first:

$\dot{x}=\frac{11x+2y}{5}$

$\dot{y}=\frac{-2x-y}{5}$

So now writing this as a first order vector ODE:

$\dot{\bold{x}}=\left[\begin{array}{cc}11/5 & 2/5\\-2/5 & -1/5\end{array}\right] {\bold{x}}$

where:

${\bold{x}}=\left[\begin{array}{c}x\\y\end{array}\right]$

So now can you get ode45 to work?

CB

The following users thank CaptainBlack for this useful post:
Rapha
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