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 = 0.0587366 (sec), leaf count = 76
\[\left \{\left \{y(x)\to c_1 e^{-2 x} x^2-\frac {2 c_2 e^{-2 x} \left (e^{2 x} \left (16 x^2+4 x+3\right )-16 \sqrt {2 \pi } x^{5/2} \text {erfi}\left (\sqrt {2} \sqrt {x}\right )\right )}{15 \sqrt {x}}\right \}\right \}\]
Maple ✓
cpu = 0.13 (sec), leaf count = 51
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-2\,x}}{x}^{2}-16\,{\frac {{\it \_C2}\, \left ( -{x}^{5/2}\sqrt {2}\sqrt {\pi }{\it erfi} \left ( \sqrt {2}\sqrt {x} \right ) {{\rm e}^{-2\,x}}+{x}^{2}+x/4+3/16 \right ) }{\sqrt {x}}} \right \} \] 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*Pi]*x^(5/2)*Erfi[Sqrt[2]*Sqrt[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),'implicit')
Maple raw output
y(x) = _C1*exp(-2*x)*x^2-16*_C2/x^(1/2)*(-x^(5/2)*2^(1/2)*Pi^(1/2)*erfi(2^(1/2)*x^(1/2))*exp(-2*x)+x^2+1/4*x+3/16)