ODE No. 1150

\[ x^2 y''(x)+\left (x^2-2\right ) y(x)=0 \] Mathematica : cpu = 0.0069983 (sec), leaf count = 53

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

\[\left \{\left \{y(x)\to \sqrt {\frac {2}{\pi }} c_2 \left (-\sin (x)-\frac {\cos (x)}{x}\right )+\sqrt {\frac {2}{\pi }} c_1 \left (\frac {\sin (x)}{x}-\cos (x)\right )\right \}\right \}\] Maple : cpu = 0.073 (sec), leaf count = 27

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

\[y \left (x \right ) = \frac {\left (c_{1} x +c_{2}\right ) \cos \left (x \right )+\sin \left (x \right ) \left (x c_{2}-c_{1}\right )}{x}\]