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 = 0.175678 (sec), leaf count = 22
\[\left \{\left \{y(x)\to \frac {c_2 x+c_1}{x^3+x^2}\right \}\right \}\]
Maple ✓
cpu = 0.057 (sec), leaf count = 19
\[\left [y \left (x \right ) = \frac {\textit {\_C1} x +\textit {\_C2}}{x^{3}+x^{2}}\right ]\] 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*(x+1)*diff(diff(y(x),x),x)+2*x*(2+3*x)*diff(y(x),x)+2*(1+3*x)*y(x) = 0, y(x))
Maple raw output
[y(x) = (_C1*x+_C2)/(x^3+x^2)]