ODE
\[ 2 x^2 y''(x)-(1-4 x) x y'(x)-2 (1-3 x) y(x)=x^3 (x+1) \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.904258 (sec), leaf count = 83
\[\left \{\left \{y(x)\to \frac {1}{252} (14 x+11) x^2+c_1 e^{-2 x} x^2-\frac {2 c_2 e^{-2 x} \left (e^{2 x} \left (16 x^2+4 x+3\right )-16 \sqrt {2} (-x)^{5/2} \Gamma \left (\frac {1}{2},-2 x\right )\right )}{15 \sqrt {x}}\right \}\right \}\]
Maple ✓
cpu = 0.658 (sec), leaf count = 62
\[\left [y \left (x \right ) = x^{2} {\mathrm e}^{-2 x} \textit {\_C2} +\frac {\left (16 \erfi \left (\sqrt {2}\, \sqrt {x}\right ) \sqrt {2}\, \sqrt {\pi }\, x^{\frac {5}{2}} {\mathrm e}^{-2 x}-16 x^{2}-4 x -3\right ) \textit {\_C1}}{\sqrt {x}}+\frac {x^{3}}{18}+\frac {11 x^{2}}{252}\right ]\] Mathematica raw input
DSolve[-2*(1 - 3*x)*y[x] - (1 - 4*x)*x*y'[x] + 2*x^2*y''[x] == x^3*(1 + x),y[x],x]
Mathematica raw output
{{y[x] -> (x^2*(11 + 14*x))/252 + (x^2*C[1])/E^(2*x) - (2*C[2]*(E^(2*x)*(3 + 4*x + 16*x^2) - 16*Sqrt[2]*(-x)^(5/2)*Gamma[1/2, -2*x]))/(15*E^(2*x)*Sqrt[x])}}
Maple raw input
dsolve(2*x^2*diff(diff(y(x),x),x)-x*(1-4*x)*diff(y(x),x)-2*(1-3*x)*y(x) = x^3*(x+1), y(x))
Maple raw output
[y(x) = x^2*exp(-2*x)*_C2+(16*erfi(2^(1/2)*x^(1/2))*2^(1/2)*Pi^(1/2)*x^(5/2)*exp(-2*x)-16*x^2-4*x-3)/x^(1/2)*_C1+1/18*x^3+11/252*x^2]