4.4.29 \(x y'(x)=x^3+\left (2 x^2+1\right ) y(x)+x y(x)^2\)

ODE
\[ x y'(x)=x^3+\left (2 x^2+1\right ) y(x)+x y(x)^2 \] ODE Classification

[[_homogeneous, `class D`], _rational, _Riccati]

Book solution method
Riccati ODE, Generalized ODE

Mathematica
cpu = 0.0119542 (sec), leaf count = 27

\[\left \{\left \{y(x)\to -\frac {x \left (2 c_1+x^2+2\right )}{2 c_1+x^2}\right \}\right \}\]

Maple
cpu = 0.014 (sec), leaf count = 21

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

DSolve[x*y'[x] == x^3 + (1 + 2*x^2)*y[x] + x*y[x]^2,y[x],x]

Mathematica raw output

{{y[x] -> -((x*(2 + x^2 + 2*C[1]))/(x^2 + 2*C[1]))}}

Maple raw input

dsolve(x*diff(y(x),x) = x^3+(2*x^2+1)*y(x)+x*y(x)^2, y(x),'implicit')

Maple raw output

-x/(x+y(x))-1/2*x^2-_C1 = 0