Solve system of 2 nonlinear second order ODEs

Hello guys!

I'm having some troubles to solve this (I don't even know if Matlab does this easily). Can you please give me a couple of tips?

So, the two equations are (where c1,c2,.. are constants and y',y'' are the first and second derivatives of y):

     H² = (8pi/3)[(1 + x)³(1 + c1*exp(-2*y)) + (1 + x)⁴ + c2*(y')² + c3]
     y'' + 3*H*y' = -c4*(1 + x)³*exp(-2*y)

Thank you so much!

Answer 1

[Star Strider]

MATLAB can probably solve it easily, but that depends on what the system of equations does. (You may need to experiment with different solvers.) First, see the MIT handout on the Companion Matrix. You will need to understand this to set up your second equation as a system of two first-order differential equations. See the documentation for ode45 to understand how to code the equations you derived. It is actually straightforward.

You might want to consider that your first equation calculates H², but the second uses H. What root of H² do you want to use?