ODE
\[ 2 x^2 y''(x)-(1-4 x) x y'(x)-2 (1-3 x) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.234076 (sec), leaf count = 71
\[\left \{\left \{y(x)\to c_1 e^{-2 x} x^2-\frac {2 c_2 e^{-2 x} \left (e^{2 x} \left (16 x^2+4 x+3\right )-16 \sqrt {2} (-x)^{5/2} \Gamma \left (\frac {1}{2},-2 x\right )\right )}{15 \sqrt {x}}\right \}\right \}\]
Maple ✓
cpu = 0.728 (sec), leaf count = 52
\[\left [y \left (x \right ) = \textit {\_C1} \,x^{2} {\mathrm e}^{-2 x}+\frac {\textit {\_C2} \left (16 \erfi \left (\sqrt {2}\, \sqrt {x}\right ) \sqrt {2}\, \sqrt {\pi }\, x^{\frac {5}{2}} {\mathrm e}^{-2 x}-16 x^{2}-4 x -3\right )}{\sqrt {x}}\right ]\] Mathematica raw input
DSolve[-2*(1 - 3*x)*y[x] - (1 - 4*x)*x*y'[x] + 2*x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (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) = 0, y(x))
Maple raw output
[y(x) = _C1*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)]