ODE
\[ \left (x^2+3 x+4\right ) y''(x)+\left (x^2+x+1\right ) y'(x)-((2 x+3) y(x))=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.213937 (sec), leaf count = 23
\[\left \{\left \{y(x)\to c_2 \left (x^2+x+3\right )+c_1 e^{-x}\right \}\right \}\]
Maple ✓
cpu = 0.076 (sec), leaf count = 19
\[[y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{-x}+\textit {\_C2} \left (x^{2}+x +3\right )]\] Mathematica raw input
DSolve[-((3 + 2*x)*y[x]) + (1 + x + x^2)*y'[x] + (4 + 3*x + x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]/E^x + (3 + x + x^2)*C[2]}}
Maple raw input
dsolve((x^2+3*x+4)*diff(diff(y(x),x),x)+(x^2+x+1)*diff(y(x),x)-(3+2*x)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*exp(-x)+_C2*(x^2+x+3)]