ODE
\[ 2 x y(x) y'(x)=x^2+y(x)^2 \] ODE Classification
[[_homogeneous, `class A`], _rational, _Bernoulli]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.00717018 (sec), leaf count = 38
\[\left \{\left \{y(x)\to -\sqrt {x} \sqrt {c_1+x}\right \},\left \{y(x)\to \sqrt {x} \sqrt {c_1+x}\right \}\right \}\]
Maple ✓
cpu = 0.005 (sec), leaf count = 14
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{2}- \left ( x+{\it \_C1} \right ) x=0 \right \} \] Mathematica raw input
DSolve[2*x*y[x]*y'[x] == x^2 + y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> -(Sqrt[x]*Sqrt[x + C[1]])}, {y[x] -> Sqrt[x]*Sqrt[x + C[1]]}}
Maple raw input
dsolve(2*x*y(x)*diff(y(x),x) = x^2+y(x)^2, y(x),'implicit')
Maple raw output
y(x)^2-(x+_C1)*x = 0