ODE
\[ x (x+1) y''(x)+(3 x+2) y'(x)+y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0621307 (sec), leaf count = 28
\[\left \{\left \{y(x)\to \frac {c_2 \log (2 (x+1))+2 c_1}{\sqrt {2} x}\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 16
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\,\ln \left ( 1+x \right ) +{\it \_C2}}{x}} \right \} \] Mathematica raw input
DSolve[y[x] + (2 + 3*x)*y'[x] + x*(1 + x)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (2*C[1] + C[2]*Log[2*(1 + x)])/(Sqrt[2]*x)}}
Maple raw input
dsolve(x*(1+x)*diff(diff(y(x),x),x)+(2+3*x)*diff(y(x),x)+y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (_C1*ln(1+x)+_C2)/x