4.34.41 \((x+1) x^2 y''(x)+2 (3 x+2) x y'(x)+2 (3 x+1) y(x)=0\)

ODE
\[ (x+1) x^2 y''(x)+2 (3 x+2) x y'(x)+2 (3 x+1) y(x)=0 \] ODE Classification

[[_2nd_order, _exact, _linear, _homogeneous]]

Book solution method
TO DO

Mathematica
cpu = 0.0251195 (sec), leaf count = 22

\[\left \{\left \{y(x)\to \frac {c_2 x+c_1}{x^3+x^2}\right \}\right \}\]

Maple
cpu = 0.021 (sec), leaf count = 18

\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\,x+{\it \_C2}}{{x}^{2} \left ( 1+x \right ) }} \right \} \] Mathematica raw input

DSolve[2*(1 + 3*x)*y[x] + 2*x*(2 + 3*x)*y'[x] + x^2*(1 + x)*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (C[1] + x*C[2])/(x^2 + x^3)}}

Maple raw input

dsolve(x^2*(1+x)*diff(diff(y(x),x),x)+2*x*(2+3*x)*diff(y(x),x)+2*(1+3*x)*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = (_C1*x+_C2)/x^2/(1+x)