ODE
\[ 2 y(x) y'(x)=x^3+x y(x)^2 \] ODE Classification
[_rational, _Bernoulli]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.227979 (sec), leaf count = 57
\[\left \{\left \{y(x)\to -\sqrt {-x^2+c_1 e^{\frac {x^2}{2}}-2}\right \},\left \{y(x)\to \sqrt {-x^2+c_1 e^{\frac {x^2}{2}}-2}\right \}\right \}\]
Maple ✓
cpu = 0.023 (sec), leaf count = 43
\[\left [y \left (x \right ) = \sqrt {{\mathrm e}^{\frac {x^{2}}{2}} \textit {\_C1} -x^{2}-2}, y \left (x \right ) = -\sqrt {{\mathrm e}^{\frac {x^{2}}{2}} \textit {\_C1} -x^{2}-2}\right ]\] 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))
Maple raw output
[y(x) = (exp(1/2*x^2)*_C1-x^2-2)^(1/2), y(x) = -(exp(1/2*x^2)*_C1-x^2-2)^(1/2)]