4.10.14 \(2 y(x) y'(x)=x^3+x y(x)^2\)

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

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