4.11.49 \(3 x^2+(2 x y(x)-x+3) y'(x)+y(x)^2-y(x)=0\)

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

[_exact, _rational, [_Abel, `2nd type``class B`]]

Book solution method
Exact equation

Mathematica
cpu = 0.0111792 (sec), leaf count = 75

\[\left \{\left \{y(x)\to -\frac {\sqrt {4 c_1 x-4 x^4+x^2-6 x+9}-x+3}{2 x}\right \},\left \{y(x)\to \frac {\sqrt {\left (4 c_1-6\right ) x-4 x^4+x^2+9}+x-3}{2 x}\right \}\right \}\]

Maple
cpu = 0.014 (sec), leaf count = 22

\[ \left \{ x \left (y \relax (x ) \right ) ^{2}+ \left (3-x \right ) y \relax (x ) +{x}^{3}+{\it \_C1}=0 \right \} \] Mathematica raw input

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

Mathematica raw output

{{y[x] -> -(3 - x + Sqrt[9 - 6*x + x^2 - 4*x^4 + 4*x*C[1]])/(2*x)}, {y[x] -> (-3
 + x + Sqrt[9 + x^2 - 4*x^4 + x*(-6 + 4*C[1])])/(2*x)}}

Maple raw input

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

Maple raw output

x*y(x)^2+(3-x)*y(x)+x^3+_C1 = 0