Solving non linear ODE ?

I am trying to solve a non-linear ODE

(y'')^2- y^2*(1+y'^2)^(3/2)=0

with boundary conditions: at x=0, y'=0 at x=1, y'= 1

How should I use ode45 or bvp4c to solve this problem ? Thanks

Answer 1

[Torsten]

function nlinbvp4c

solinit = bvpinit(linspace(0,1,5),[0 0]);
sol = bvp4c(@twoode,@twobc,solinit);

function dydx = twoode(x,y)
dydx = [ y(2); abs(y(1))*(1+y(2)^2)^0.75 ];

function res = twobc(ya,yb)
res = [ ya(2); yb(2) - 1 ];

Not sure, but when solving for y'', you may also take the negative square root of the right-hand side:

y''=-abs(y(1))*(1+y(2)^2)^0.75

Thus there might be two solutions for your problem.

Best wishes

Torsten.