2.1115   ODE No. 1115

\[ x y''(x)-(3 x-2) y'(x)+(3-2 x) y(x)=0 \] Mathematica : cpu = 0.0344987 (sec), leaf count = 76

DSolve[(3 - 2*x)*y[x] - (-2 + 3*x)*Derivative[1][y][x] + x*Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_2 e^{-\frac {1}{2} \left (\sqrt {17}-3\right ) x} \operatorname {Hypergeometric1F1}\left (1-\frac {6}{\sqrt {17}},2,\sqrt {17} x\right )+c_1 e^{-\frac {1}{2} \left (\sqrt {17}-3\right ) x} \operatorname {HypergeometricU}\left (1-\frac {6}{\sqrt {17}},2,\sqrt {17} x\right )\right \}\right \}\] Maple : cpu = 1.642 (sec), leaf count = 47

dsolve(x*diff(diff(y(x),x),x)-(3*x-2)*diff(y(x),x)-(2*x-3)*y(x)=0,y(x))
 

\[y \left (x \right ) = {\mathrm e}^{-\frac {x \left (-3+\sqrt {17}\right )}{2}} \left (\operatorname {KummerM}\left (1-\frac {6 \sqrt {17}}{17}, 2, \sqrt {17}\, x \right ) c_{1}+\operatorname {KummerU}\left (1-\frac {6 \sqrt {17}}{17}, 2, \sqrt {17}\, x \right ) c_{2}\right )\]