ODE
\[ 2 y(x) y'(x)=x^3+x y(x)^2 \] ODE Classification
[_rational, _Bernoulli]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.0115853 (sec), leaf count = 57
\[\left \{\left \{y(x)\to -\sqrt {c_1 e^{\frac {x^2}{2}}-x^2-2}\right \},\left \{y(x)\to \sqrt {c_1 e^{\frac {x^2}{2}}-x^2-2}\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 21
\[ \left \{ {x}^{2}+2-{{\rm e}^{{\frac {{x}^{2}}{2}}}}{\it \_C1}+ \left ( y \left ( x \right ) \right ) ^{2}=0 \right \} \] Mathematica raw input
DSolve[2*y[x]*y'[x] == x^3 + x*y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> -Sqrt[-2 - x^2 + E^(x^2/2)*C[1]]}, {y[x] -> Sqrt[-2 - x^2 + E^(x^2/2)*C[1]]}}
Maple raw input
dsolve(2*y(x)*diff(y(x),x) = x*y(x)^2+x^3, y(x),'implicit')
Maple raw output
x^2+2-exp(1/2*x^2)*_C1+y(x)^2 = 0