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 = 0.174841 (sec), leaf count = 41
\[\left \{\left \{y(x)\to \frac {-3 x^2+2 (x+1)^2 \log (x+1)+(-2+4 c_2) x+4 c_1}{4 x^2}\right \}\right \}\]
Maple ✓
cpu = 0.124 (sec), leaf count = 52
\[\left [y \left (x \right ) = \frac {\textit {\_C1}}{x}+\frac {\textit {\_C2}}{x^{2}}+\frac {2 \ln \left (x +1\right ) x^{2}+4 \ln \left (x +1\right ) x -3 x^{2}+2 \ln \left (x +1\right )-6 x -1}{4 x^{2}}\right ]\] 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 + 4*C[1] + x*(-2 + 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(x+1), y(x))
Maple raw output
[y(x) = 1/x*_C1+1/x^2*_C2+1/4*(2*ln(x+1)*x^2+4*ln(x+1)*x-3*x^2+2*ln(x+1)-6*x-1)/x^2]