Analytical solution for coupled ODE's

[charudatta]

Hello all,

I wanted to know if there are ways to find analytical solutions for a set of equations defined as follows:

1) x''(z) + B(y,z)*y'(z) + C(y,z) = 0
2) y''(z) + B(y,z)*x'(z) = 0

where ' represents derivative wrt z. and we need to determine y(z) and x(z). B(y,z) and C(y,z) are known functions.

the only way i could think of is converting the 2 eqns into 4 first order equations by defining x'(z) = a(z) and y'(z) = b(z) and solve numerically.
Thanks in advance...

cheers,
-cd

 

[arildno]

Well, on most places, you may replace x'=y''/B(y,z). Differentiating with respect to z, you'll end up with a third-order non-linear equation for y.