ODE
\[ x^2 y''(x)+4 x y'(x)+2 y(x)=\log (x+1) \] ODE Classification
[[_2nd_order, _exact, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0162777 (sec), leaf count = 41
\[\left \{\left \{y(x)\to \frac {\left (4 c_1-2\right ) x+4 c_2-3 x^2+2 (x+1)^2 \log (x+1)}{4 x^2}\right \}\right \}\]
Maple ✓
cpu = 0.016 (sec), leaf count = 37
\[ \left \{ y \left ( x \right ) ={\frac {2\,\ln \left ( 1+x \right ) \left ( 1+x \right ) ^{2}-3\,{x}^{2}+ \left ( 4\,{\it \_C1}-6 \right ) x+4\,{\it \_C2}-1}{4\,{x}^{2}}} \right \} \] Mathematica raw input
DSolve[2*y[x] + 4*x*y'[x] + x^2*y''[x] == Log[1 + x],y[x],x]
Mathematica raw output
{{y[x] -> (-3*x^2 + x*(-2 + 4*C[1]) + 4*C[2] + 2*(1 + x)^2*Log[1 + x])/(4*x^2)}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+4*x*diff(y(x),x)+2*y(x) = ln(1+x), y(x),'implicit')
Maple raw output
y(x) = 1/4*(2*ln(1+x)*(1+x)^2-3*x^2+(4*_C1-6)*x+4*_C2-1)/x^2