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 = 0.177435 (sec), leaf count = 32
\[\left \{\left \{y(x)\to \frac {x^2}{2}+c_1\right \},\left \{y(x)\to -x+c_1 e^{-x}+1\right \}\right \}\]
Maple ✓
cpu = 0.047 (sec), leaf count = 25
\[\left [y \left (x \right ) = \frac {x^{2}}{2}+\textit {\_C1}, y \left (x \right ) = -x +1+\textit {\_C1} \,{\mathrm e}^{-x}\right ]\] 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))
Maple raw output
[y(x) = 1/2*x^2+_C1, y(x) = -x+1+_C1*exp(-x)]