4.11.46 \(2 x y(x) y'(x)=x^2+y(x)^2\)

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

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