4.40.1 \(2 y(x) y''(x)=-a^2-4 \left (b-x^2\right ) y(x)^2+y'(x)^2+3 y(x)^4+8 x y(x)^3\)

ODE
\[ 2 y(x) y''(x)=-a^2-4 \left (b-x^2\right ) y(x)^2+y'(x)^2+3 y(x)^4+8 x y(x)^3 \] ODE Classification

[[_Painleve, `4th`]]

Book solution method
TO DO

Mathematica
cpu = 1.32384 (sec), leaf count = 0 , could not solve

DSolve[2*y[x]*Derivative[2][y][x] == -a^2 - 4*(b - x^2)*y[x]^2 + 8*x*y[x]^3 + 3*y[x]^4 + Derivative[1][y][x]^2, y[x], x]

Maple
cpu = 0.371 (sec), leaf count = 0 , could not solve

dsolve(2*y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2-a^2-4*(-x^2+b)*y(x)^2+8*x*y(x)^3+3*y(x)^4, y(x),'implicit')

Mathematica raw input

DSolve[2*y[x]*y''[x] == -a^2 - 4*(b - x^2)*y[x]^2 + 8*x*y[x]^3 + 3*y[x]^4 + y'[x]^2,y[x],x]

Mathematica raw output

DSolve[2*y[x]*Derivative[2][y][x] == -a^2 - 4*(b - x^2)*y[x]^2 + 8*x*y[x]^3 + 3*
y[x]^4 + Derivative[1][y][x]^2, y[x], x]

Maple raw input

dsolve(2*y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2-a^2-4*(-x^2+b)*y(x)^2+8*x*y(x)^3+3*y(x)^4, y(x),'implicit')

Maple raw output

dsolve(2*y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2-a^2-4*(-x^2+b)*y(x)^2+8*x*y(
x)^3+3*y(x)^4, y(x),'implicit')