ODE
\[ \left (x^2+y(x)^2\right ) y'(x)=x y(x) \] ODE Classification
[[_homogeneous, `class A`], _rational, _dAlembert]
Book solution method
Homogeneous equation
Mathematica ✓
cpu = 0.310562 (sec), leaf count = 44
\[\left \{\left \{y(x)\to -\frac {x}{\sqrt {W\left (e^{-2 c_1} x^2\right )}}\right \},\left \{y(x)\to \frac {x}{\sqrt {W\left (e^{-2 c_1} x^2\right )}}\right \}\right \}\]
Maple ✓
cpu = 0.09 (sec), leaf count = 16
\[\left [y \left (x \right ) = \sqrt {\frac {1}{\LambertW \left (x^{2} \textit {\_C1} \right )}}\, x\right ]\] Mathematica raw input
DSolve[(x^2 + y[x]^2)*y'[x] == x*y[x],y[x],x]
Mathematica raw output
{{y[x] -> -(x/Sqrt[ProductLog[x^2/E^(2*C[1])]])}, {y[x] -> x/Sqrt[ProductLog[x^2/E^(2*C[1])]]}}
Maple raw input
dsolve((x^2+y(x)^2)*diff(y(x),x) = x*y(x), y(x))
Maple raw output
[y(x) = (1/LambertW(x^2*_C1))^(1/2)*x]