4.17.12 \(y'(x)^2+y(x) y'(x)=x (y(x)+x)\)

ODE
\[ y'(x)^2+y(x) y'(x)=x (y(x)+x) \] ODE Classification

[_quadrature]

Book solution method
No Missing Variables ODE, Solve for \(y'\)

Mathematica
cpu = 0.00528489 (sec), leaf count = 32

\[\left \{\left \{y(x)\to c_1+\frac {x^2}{2}\right \},\left \{y(x)\to c_1 e^{-x}-x+1\right \}\right \}\]

Maple
cpu = 0.008 (sec), leaf count = 25

\[ \left \{ y \relax (x ) ={\frac {{x}^{2}}{2}}+{\it \_C1},y \relax (x ) =-x+1+{{\rm e}^{-x}}{\it \_C1} \right \} \] Mathematica raw input

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

Mathematica raw output

{{y[x] -> x^2/2 + C[1]}, {y[x] -> 1 - x + C[1]/E^x}}

Maple raw input

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

Maple raw output

y(x) = 1/2*x^2+_C1, y(x) = -x+1+exp(-x)*_C1