4.8.4 \(x^3 y'(x)=y(x) \left (2 x^2+y(x)^2\right )\)

ODE
\[ x^3 y'(x)=y(x) \left (2 x^2+y(x)^2\right ) \] ODE Classification

[[_homogeneous, `class A`], _rational, _Bernoulli]

Book solution method
Homogeneous equation

Mathematica
cpu = 0.00845715 (sec), leaf count = 42

\[\left \{\left \{y(x)\to -\frac {x^2}{\sqrt {c_1-x^2}}\right \},\left \{y(x)\to \frac {x^2}{\sqrt {c_1-x^2}}\right \}\right \}\]

Maple
cpu = 0.007 (sec), leaf count = 17

\[ \left \{ {x}^{-2}-{\frac {{\it \_C1}}{{x}^{4}}}+ \left (y \relax (x ) \right ) ^{-2}=0 \right \} \] Mathematica raw input

DSolve[x^3*y'[x] == y[x]*(2*x^2 + y[x]^2),y[x],x]

Mathematica raw output

{{y[x] -> -(x^2/Sqrt[-x^2 + C[1]])}, {y[x] -> x^2/Sqrt[-x^2 + C[1]]}}

Maple raw input

dsolve(x^3*diff(y(x),x) = (2*x^2+y(x)^2)*y(x), y(x),'implicit')

Maple raw output

1/x^2-1/x^4*_C1+1/y(x)^2 = 0