#### 4.695

ODE

ODE Classification

[[_homogeneous, `class G`], _rational]

Book solution method
Exact equation, integrating factor

Mathematica
cpu = 0.127114 (sec), leaf count = 359

Maple
cpu = 0.021 (sec), leaf count = 33

Mathematica raw input

DSolve[x*(x - y[x]^3)*y'[x] == y[x]*(3*x + y[x]^3),y[x],x]

Mathematica raw output

{{y[x] -> (-9*x^7 + Sqrt[3]*Sqrt[-(x^6*(E^(8*C[1]) - 27*x^8))])^(1/3)/(3^(2/3)*x
^2) + E^((8*C[1])/3)/(-27*x^7 + 3*Sqrt[3]*Sqrt[-(x^6*(E^(8*C[1]) - 27*x^8))])^(1
/3)}, {y[x] -> (-((3*I + Sqrt[3])*E^((8*C[1])/3)*x^2) + I*3^(1/6)*(I + Sqrt[3])*
(-9*x^7 + Sqrt[3]*Sqrt[-(x^6*(E^(8*C[1]) - 27*x^8))])^(2/3))/(2*3^(5/6)*x^2*(-9*
x^7 + Sqrt[3]*Sqrt[-(x^6*(E^(8*C[1]) - 27*x^8))])^(1/3))}, {y[x] -> (I*3^(1/3)*(
I + Sqrt[3])*E^((8*C[1])/3) + ((-1 - I*Sqrt[3])*(-9*x^7 + Sqrt[3]*Sqrt[-(x^6*(E^
(8*C[1]) - 27*x^8))])^(2/3))/x^2)/(2*3^(2/3)*(-9*x^7 + Sqrt[3]*Sqrt[-(x^6*(E^(8*
C[1]) - 27*x^8))])^(1/3))}}

Maple raw input

dsolve(x*(x-y(x)^3)*diff(y(x),x) = (3*x+y(x)^3)*y(x), y(x),'implicit')

Maple raw output

ln(x)-_C1+3/8*ln((y(x)^3+2*x)/x)-3/8*ln(1/x^(1/3)*y(x)) = 0