4.11.43 \(a+2 x y(x) y'(x)+y(x)^2=0\)

ODE
\[ a+2 x y(x) y'(x)+y(x)^2=0 \] ODE Classification

[_separable]

Book solution method
Exact equation

Mathematica ✓
cpu = 0.0124835 (sec), leaf count = 52

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

Maple ✓
cpu = 0.005 (sec), leaf count = 15

\[ \left \{ a-{\frac {{\it \_C1}}{x}}+ \left ( y \left ( x \right ) \right ) ^{2}=0 \right \} \] Mathematica raw input

DSolve[a + y[x]^2 + 2*x*y[x]*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -(Sqrt[E^(2*C[1]) - a*x]/Sqrt[x])}, {y[x] -> Sqrt[E^(2*C[1]) - a*x]/Sq
rt[x]}}

Maple raw input

dsolve(2*x*y(x)*diff(y(x),x)+a+y(x)^2 = 0, y(x),'implicit')

Maple raw output

a-1/x*_C1+y(x)^2 = 0