MATLAB: Solving non linear ODE

bvp4code45

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

Best Answer

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.
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