2.1191   ODE No. 1191

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

✓ Mathematica : cpu = 0.0065904 (sec), leaf count = 110

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

\[\left \{\left \{y(x)\to \frac {2 c_2 e^{\frac {1}{2} (\log (x)-x)} \left (i \sinh \left (\frac {x}{2}\right )-\frac {2 i \cosh \left (\frac {x}{2}\right )}{x}\right )}{\sqrt {\pi } \sqrt {-i x}}+\frac {2 c_1 e^{\frac {1}{2} (\log (x)-x)} \left (\frac {2 \sinh \left (\frac {x}{2}\right )}{x}-\cosh \left (\frac {x}{2}\right )\right )}{\sqrt {\pi } \sqrt {-i x}}\right \}\right \}\]

✓ Maple : cpu = 0.024 (sec), leaf count = 23

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

\[y \left (x \right ) = \frac {c_{2} \left (x +2\right ) {\mathrm e}^{-x}+c_{1} \left (x -2\right )}{x}\]