4.9.20 \(y(x) y'(x)+x=0\)

ODE
\[ y(x) y'(x)+x=0 \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.00544579 (sec), leaf count = 39

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

Maple
cpu = 0.004 (sec), leaf count = 14

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

Maple raw output

x^2+y(x)^2-_C1 = 0