4.9.21 \(e^{x^2} x+y(x) y'(x)=0\)

ODE
\[ e^{x^2} x+y(x) y'(x)=0 \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.00882513 (sec), leaf count = 43

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

Maple
cpu = 0.006 (sec), leaf count = 15

\[ \left \{ \left (y \relax (x ) \right ) ^{2}+{{\rm e}^{{x}^{2}}}-{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

y(x)^2+exp(x^2)-_C1 = 0