ODE
\[ y(x) y'(x)+x=0 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.166606 (sec), leaf count = 39
\[\left \{\left \{y(x)\to -\sqrt {-x^2+2 c_1}\right \},\left \{y(x)\to \sqrt {-x^2+2 c_1}\right \}\right \}\]
Maple ✓
cpu = 0.016 (sec), leaf count = 27
\[\left [y \left (x \right ) = \sqrt {-x^{2}+\textit {\_C1}}, y \left (x \right ) = -\sqrt {-x^{2}+\textit {\_C1}}\right ]\] Mathematica raw input
DSolve[x + y[x]*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -Sqrt[-x^2 + 2*C[1]]}, {y[x] -> Sqrt[-x^2 + 2*C[1]]}}
Maple raw input
dsolve(y(x)*diff(y(x),x)+x = 0, y(x))
Maple raw output
[y(x) = (-x^2+_C1)^(1/2), y(x) = -(-x^2+_C1)^(1/2)]