ODE
\[ 2 y(x) y''(x)=2 x f(x) y(x)^2-4 y(x)^2 y'(x)+y'(x)^2-y(x)^4-1 \] ODE Classification
[NONE]
Book solution method
TO DO
Mathematica ✗
cpu = 0.206136 (sec), leaf count = 0 , could not solve
DSolve[2*y[x]*Derivative[2][y][x] == -1 + 2*x*f[x]*y[x]^2 - y[x]^4 - 4*y[x]^2*Derivative[1][y][x] + Derivative[1][y][x]^2, y[x], x]
Maple ✗
cpu = 0.84 (sec), leaf count = 0 , could not solve
dsolve(2*y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2-4*y(x)^2*diff(y(x),x)-1+2*f(x)*x*y(x)^2-y(x)^4, y(x))
Mathematica raw input
DSolve[2*y[x]*y''[x] == -1 + 2*x*f[x]*y[x]^2 - y[x]^4 - 4*y[x]^2*y'[x] + y'[x]^2,y[x],x]
Mathematica raw output
DSolve[2*y[x]*Derivative[2][y][x] == -1 + 2*x*f[x]*y[x]^2 - y[x]^4 - 4*y[x]^2*Derivative[1][y][x] + 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)^2-4*y(x)^2*diff(y(x),x)-1+2*f(x)*x*y(x)^2-y(x)^4, y(x))
Maple raw output
dsolve(2*y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2-4*y(x)^2*diff(y(x),x)-1+2*f(x)*x*y(x)^2-y(x)^4, y(x))