ODE
\[ a y(x)+x^2 y''(x)-2 (1-x) y'(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.216029 (sec), leaf count = 145
\[\left \{\left \{y(x)\to 2^{\frac {1}{2}-\frac {1}{2} \sqrt {1-4 a}} \left (\frac {1}{x}\right )^{\frac {1}{2}-\frac {1}{2} \sqrt {1-4 a}} \left (2^{\sqrt {1-4 a}} c_2 \left (\frac {1}{x}\right )^{\sqrt {1-4 a}} \, _1F_1\left (\frac {1}{2} \left (\sqrt {1-4 a}+1\right );\sqrt {1-4 a}+1;-\frac {2}{x}\right )+c_1 \, _1F_1\left (\frac {1}{2}-\frac {1}{2} \sqrt {1-4 a};1-\sqrt {1-4 a};-\frac {2}{x}\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.185 (sec), leaf count = 57
\[\left [y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{-\frac {1}{x}} \sqrt {\frac {1}{x}}\, \BesselI \left (\frac {\sqrt {1-4 a}}{2}, \frac {1}{x}\right )+\textit {\_C2} \,{\mathrm e}^{-\frac {1}{x}} \sqrt {\frac {1}{x}}\, \BesselK \left (\frac {\sqrt {1-4 a}}{2}, \frac {1}{x}\right )\right ]\] Mathematica raw input
DSolve[a*y[x] - 2*(1 - x)*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> 2^(1/2 - Sqrt[1 - 4*a]/2)*(x^(-1))^(1/2 - Sqrt[1 - 4*a]/2)*(C[1]*Hypergeometric1F1[1/2 - Sqrt[1 - 4*a]/2, 1 - Sqrt[1 - 4*a], -2/x] + 2^Sqrt[1 - 4*a]*(x^(-1))^Sqrt[1 - 4*a]*C[2]*Hypergeometric1F1[(1 + Sqrt[1 - 4*a])/2, 1 + Sqrt[1 - 4*a], -2/x])}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)-2*(1-x)*diff(y(x),x)+a*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*exp(-1/x)*(1/x)^(1/2)*BesselI(1/2*(1-4*a)^(1/2),1/x)+_C2*exp(-1/x)*(1/x)^(1/2)*BesselK(1/2*(1-4*a)^(1/2),1/x)]