ODE
\[ x^2 y''(x)-\left (2-x^2\right ) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00824444 (sec), leaf count = 42
\[\left \{\left \{y(x)\to -\frac {\sqrt {\frac {2}{\pi }} \left (\left (c_2 x-c_1\right ) \sin (x)+\left (c_1 x+c_2\right ) \cos (x)\right )}{x}\right \}\right \}\]
Maple ✓
cpu = 0.087 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) ={\frac { \left ( {\it \_C1}\,x+{\it \_C2} \right ) \cos \left ( x \right ) +\sin \left ( x \right ) \left ( {\it \_C2}\,x-{\it \_C1} \right ) }{x}} \right \} \] Mathematica raw input
DSolve[-((2 - x^2)*y[x]) + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -((Sqrt[2/Pi]*((x*C[1] + C[2])*Cos[x] + (-C[1] + x*C[2])*Sin[x]))/x)}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)-(-x^2+2)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = ((_C1*x+_C2)*cos(x)+sin(x)*(_C2*x-_C1))/x