4.11.9 \(x y(x) y'(x)=y(x)^2+x\)

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

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

Book solution method
Exact equation, integrating factor

Mathematica
cpu = 0.00641502 (sec), leaf count = 42

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

Maple
cpu = 0.007 (sec), leaf count = 17

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

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

Mathematica raw output

{{y[x] -> -(Sqrt[x]*Sqrt[-2 + x*C[1]])}, {y[x] -> Sqrt[x]*Sqrt[-2 + x*C[1]]}}

Maple raw input

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

Maple raw output

-x^2*_C1+y(x)^2+2*x = 0