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 = 21.0046 (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 = 0.755 (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))
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))
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))