ODE
\[ x (2 x y(x)+1) y'(x)+y(x) (3 x y(x)+2)=0 \] ODE Classification
[[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]
Book solution method
Homogeneous equation, isobaric equation
Mathematica ✓
cpu = 0.0131273 (sec), leaf count = 69
\[\left \{\left \{y(x)\to -\frac {\sqrt {x^2 \left (4 c_1+x\right )}+x^{3/2}}{2 x^{5/2}}\right \},\left \{y(x)\to \frac {\sqrt {x^2 \left (4 c_1+x\right )}-x^{3/2}}{2 x^{5/2}}\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 20
\[ \left \{ \ln \left ( x \right ) -{\it \_C1}+\ln \left ( xy \left ( x \right ) \left ( 1+xy \left ( x \right ) \right ) \right ) =0 \right \} \] Mathematica raw input
DSolve[y[x]*(2 + 3*x*y[x]) + x*(1 + 2*x*y[x])*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(x^(3/2) + Sqrt[x^2*(x + 4*C[1])])/(2*x^(5/2))}, {y[x] -> (-x^(3/2) + Sqrt[x^2*(x + 4*C[1])])/(2*x^(5/2))}}
Maple raw input
dsolve(x*(1+2*x*y(x))*diff(y(x),x)+(2+3*x*y(x))*y(x) = 0, y(x),'implicit')
Maple raw output
ln(x)-_C1+ln(x*y(x)*(1+x*y(x))) = 0