2.1197   ODE No. 1197

\[ (-a-x) y(x)+x^2 y''(x)-\left (x^2-2 x\right ) y'(x)=0 \]

✓ Mathematica : cpu = 0.0107481 (sec), leaf count = 78

DSolve[(-a - x)*y[x] - (-2*x + x^2)*Derivative[1][y][x] + x^2*Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 e^{\frac {1}{2} (x-\log (x))} J_{\frac {1}{2} \sqrt {4 a+1}}\left (-\frac {i x}{2}\right )+c_2 e^{\frac {1}{2} (x-\log (x))} Y_{\frac {1}{2} \sqrt {4 a+1}}\left (-\frac {i x}{2}\right )\right \}\right \}\]

✓ Maple : cpu = 0.06 (sec), leaf count = 43

dsolve(x^2*diff(diff(y(x),x),x)-(x^2-2*x)*diff(y(x),x)-(x+a)*y(x)=0,y(x))
 

\[y \left (x \right ) = \frac {{\mathrm e}^{\frac {x}{2}} \left (\operatorname {BesselK}\left (\frac {\sqrt {4 a +1}}{2}, \frac {x}{2}\right ) c_{2} +\operatorname {BesselI}\left (\frac {\sqrt {4 a +1}}{2}, \frac {x}{2}\right ) c_{1} \right )}{\sqrt {x}}\]