4.11.32 \(2 x^2+x (x-y(x)) y'(x)+3 x y(x)-y(x)^2=0\)

ODE
\[ 2 x^2+x (x-y(x)) y'(x)+3 x y(x)-y(x)^2=0 \] ODE Classification

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type``class B`]]

Book solution method
Exact equation, integrating factor

Mathematica
cpu = 0.02603 (sec), leaf count = 54

\[\left \{\left \{y(x)\to x-\frac {\sqrt {e^{2 c_1}+2 x^4}}{x}\right \},\left \{y(x)\to \frac {\sqrt {e^{2 c_1}+2 x^4}}{x}+x\right \}\right \}\]

Maple
cpu = 0.013 (sec), leaf count = 33

\[ \left \{ -{\frac {1}{4}\ln \left ({\frac {-{x}^{2}-2\,xy \relax (x ) + \left (y \relax (x ) \right ) ^{2}}{{x}^{2}}} \right ) }-\ln \relax (x ) -{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[2*x^2 + 3*x*y[x] - y[x]^2 + x*(x - y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> x - Sqrt[E^(2*C[1]) + 2*x^4]/x}, {y[x] -> x + Sqrt[E^(2*C[1]) + 2*x^4]
/x}}

Maple raw input

dsolve(x*(x-y(x))*diff(y(x),x)+2*x^2+3*x*y(x)-y(x)^2 = 0, y(x),'implicit')

Maple raw output

-1/4*ln((-x^2-2*x*y(x)+y(x)^2)/x^2)-ln(x)-_C1 = 0