Is there any clue to solve the following system of equation numerically by fourth order Runge-Kutta method?

We have two dependent variables y1 and y2 and one independent variable. The system is like this. (dy1/dx)^2 - y1*(dy1/dx) + x*(dy2/dx) = 0......(1) (dy2/dx)^2 + x*(dy2/dx)*(dy1/dx) + y2*(dy1/dx)^2=0.....(2) Initial condition y1(0)=1 and y2(0)=0 with x=0:0.1:0.9. Do we need to perform a rigorous solution procedure to solve the mentioned system of equations? If any replica program written in MATLAB is available for this type of system of equations, kindly provide me. Thanks for your kind consideration.

Answer 1

[Torsten]

If you want to use a MATLAB solver, write your system as

dy1/dx = y3
dy2/dx = y4
0= y3^2-y1*y3+x*y4
0= y4^2+x*y3*y4+y2*y3^2

and use ODE15s to solve.

Best wishes

Torsten.

[Debasish Pal]

Thanks for your answer. I and have not handled this type of systems of equation before and have not used ode15s. Can you please send me the code to solve my mentioned system of equations? Thanks for your kind consideration.

[Torsten]

It should be easy to adapt the example under

http://de.mathworks.com/help/matlab/math/ordinary-differential-equations.html#f1-670396

for your purpose.

Best wishes

Torsten.