ODE
\[ -\left (x^2+y(x)+x\right ) y'(x)^2+\left (x^2+x y(x)+y(x)\right ) y'(x)+x y'(x)^3-x y(x)=0 \] ODE Classification
[_quadrature]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.16082 (sec), leaf count = 31
\[\left \{\{y(x)\to c_1 x\},\{y(x)\to x+c_1\},\left \{y(x)\to \frac {x^2}{2}+c_1\right \}\right \}\]
Maple ✓
cpu = 0.036 (sec), leaf count = 23
\[\left [y \left (x \right ) = x \textit {\_C1}, y \left (x \right ) = x +\textit {\_C1}, y \left (x \right ) = \frac {x^{2}}{2}+\textit {\_C1}\right ]\] Mathematica raw input
DSolve[-(x*y[x]) + (x^2 + y[x] + x*y[x])*y'[x] - (x + x^2 + y[x])*y'[x]^2 + x*y'[x]^3 == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*C[1]}, {y[x] -> x + C[1]}, {y[x] -> x^2/2 + C[1]}}
Maple raw input
dsolve(x*diff(y(x),x)^3-(x+x^2+y(x))*diff(y(x),x)^2+(x^2+y(x)+x*y(x))*diff(y(x),x)-x*y(x) = 0, y(x))
Maple raw output
[y(x) = x*_C1, y(x) = x+_C1, y(x) = 1/2*x^2+_C1]