4.11.44 \(2 x y(x) y'(x)=a x+y(x)^2\)

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

[[_homogeneous, `class G`], _rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.00788918 (sec), leaf count = 44

\[\left \{\left \{y(x)\to -\sqrt {x} \sqrt {a \log (x)+c_1}\right \},\left \{y(x)\to \sqrt {x} \sqrt {a \log (x)+c_1}\right \}\right \}\]

Maple
cpu = 0.006 (sec), leaf count = 18

\[ \left \{ -\ln \relax (x ) ax+ \left (y \relax (x ) \right ) ^{2}-{\it \_C1}\,x=0 \right \} \] Mathematica raw input

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

Mathematica raw output

{{y[x] -> -(Sqrt[x]*Sqrt[C[1] + a*Log[x]])}, {y[x] -> Sqrt[x]*Sqrt[C[1] + a*Log[
x]]}}

Maple raw input

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

Maple raw output

-ln(x)*a*x+y(x)^2-_C1*x = 0