# Non linear ODE: y'' = a y + b y^3

by galuoises
Tags: linear
 P: 8 I would like to solve the non linear ODE $\frac{d}{dx}f(x)=a f(x)+ b f^3 (x)$ with the boundary $f(0)=0\quad f(+\infty)=f_0$ How to find analitical solution?
 P: 8 Pardon me, I write the uncorrect differential equation: the problem is at the second order $\frac{d^2}{dx^2}f(x)=a f(x) + b f^3 (x)$ with the boundary $f(0)=0,\ f(+\infty)=f_0$
 P: 1,666 Non linear ODE: y'' = a y + b y^3 In my opinion, $x(y)=g(y,c_1,c_2)$ is an analytical expression for the solution but I think first, just scrap the a and b and look at: $$y''=y+y^3$$ then do what Jacq said and get the expression in terms of: $$x(y)=g(y,c_1,c_2)$$ then try and solve simultaneously the expressions: $$0=g(0,c_1,c_2)$$ $$g(f_0,c_1,c_2)\to+\infty$$ for the constants $c_1,c_2$ and if need be, do so numerically for them just for starters.