solving non-linear ODEs algebraically with symbolic math toolbox

Hi! I'm trying to solve a second order nonlinear ODE for $u_n(t)$, and I have this code:

clear all

n = sym('n');

p = sym('p'); %constant

syms y(x)

d2y = diff(y,2);

dy = diff(y);

dsolve(d2y - (dy)^2/(2*y) - (3*y^3)/2 - 4*x*y^2 - 2*(x^2 + n/2 + (2*p + 1)*(1 + 3*(-1)^n)/4)*y +(n + (2*p + 1)*(1 - (-1)^n))/(4*y) == 0)

I'm getting errors:

Error using assignin Invalid variable name "y(x)" in ASSIGNIN.

Error in syms (line 47) assignin('caller',varargin{1},sym(varargin{1}));

Error in diff_eqn_recc (line 6) syms y(x)

I don't know what's causing this, can anyone help?

Thanks!

[RahulTandon]

I tried to solve your problem.Explicit Solution not found. But your errors have been removed! The problem has been rephrased!

Answer 1

[RahulTandon]

%% Rephrased your problem clc; syms n p x y(x); y = dsolve('D2y - (Dy)^2/(2*y) - (3*y^3)/2 - 4*x*y^2 - 2*(x^2 + n/2 + (2*p + 1)*(1 + 3*(-1)^n)/4)*y +(n + (2*p + 1)*(1 - (-1)^n))/(4*y) == 0','x')