ODE
\[ x \left (x^5+3 y(x)^2\right ) y'(x)-2 x^5 y(x)-3 x^2 y(x) y'(x)^2+x y'(x)^3-y(x)^3=0 \] ODE Classification
[`y=_G(x,y')`]
Book solution method
Change of variable
Mathematica ✗
cpu = 551.162 (sec), leaf count = 0 , could not solve
DSolve[-2*x^5*y[x] - y[x]^3 + x*(x^5 + 3*y[x]^2)*Derivative[1][y][x] - 3*x^2*y[x]*Derivative[1][y][x]^2 + x*Derivative[1][y][x]^3 == 0, y[x], x]
Maple ✗
cpu = 3.104 (sec), leaf count = 0 , could not solve
dsolve(x*diff(y(x),x)^3-3*x^2*y(x)*diff(y(x),x)^2+x*(x^5+3*y(x)^2)*diff(y(x),x)-2*x^5*y(x)-y(x)^3 = 0, y(x))
Mathematica raw input
DSolve[-2*x^5*y[x] - y[x]^3 + x*(x^5 + 3*y[x]^2)*y'[x] - 3*x^2*y[x]*y'[x]^2 + x*y'[x]^3 == 0,y[x],x]
Mathematica raw output
DSolve[-2*x^5*y[x] - y[x]^3 + x*(x^5 + 3*y[x]^2)*Derivative[1][y][x] - 3*x^2*y[x]*Derivative[1][y][x]^2 + x*Derivative[1][y][x]^3 == 0, y[x], x]
Maple raw input
dsolve(x*diff(y(x),x)^3-3*x^2*y(x)*diff(y(x),x)^2+x*(x^5+3*y(x)^2)*diff(y(x),x)-2*x^5*y(x)-y(x)^3 = 0, y(x))
Maple raw output
dsolve(x*diff(y(x),x)^3-3*x^2*y(x)*diff(y(x),x)^2+x*(x^5+3*y(x)^2)*diff(y(x),x)-2*x^5*y(x)-y(x)^3 = 0, y(x))