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 = 0.25034 (sec), leaf count = 38
\[\left \{\left \{y(x)\to -\sqrt {x} \sqrt {x+c_1}\right \},\left \{y(x)\to \sqrt {x} \sqrt {x+c_1}\right \}\right \}\]
Maple ✓
cpu = 0.019 (sec), leaf count = 27
\[\left [y \left (x \right ) = \sqrt {x \textit {\_C1} +x^{2}}, y \left (x \right ) = -\sqrt {x \textit {\_C1} +x^{2}}\right ]\] 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))
Maple raw output
[y(x) = (_C1*x+x^2)^(1/2), y(x) = -(_C1*x+x^2)^(1/2)]