ODE
\[ e^{x^2} x+y(x) y'(x)=0 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.183749 (sec), leaf count = 43
\[\left \{\left \{y(x)\to -\sqrt {-e^{x^2}+2 c_1}\right \},\left \{y(x)\to \sqrt {-e^{x^2}+2 c_1}\right \}\right \}\]
Maple ✓
cpu = 0.023 (sec), leaf count = 29
\[\left [y \left (x \right ) = \sqrt {-{\mathrm e}^{x^{2}}+\textit {\_C1}}, y \left (x \right ) = -\sqrt {-{\mathrm e}^{x^{2}}+\textit {\_C1}}\right ]\] Mathematica raw input
DSolve[E^x^2*x + y[x]*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -Sqrt[-E^x^2 + 2*C[1]]}, {y[x] -> Sqrt[-E^x^2 + 2*C[1]]}}
Maple raw input
dsolve(y(x)*diff(y(x),x)+x*exp(x^2) = 0, y(x))
Maple raw output
[y(x) = (-exp(x^2)+_C1)^(1/2), y(x) = -(-exp(x^2)+_C1)^(1/2)]