ODE
\[ x^2 y''(x)+\left (2-x^2\right ) y(x)+4 x y'(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00952535 (sec), leaf count = 28
\[\left \{\left \{y(x)\to \frac {2 c_1 e^{-x}+c_2 e^x}{2 x^2}\right \}\right \}\]
Maple ✓
cpu = 0.036 (sec), leaf count = 17
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C2}\,\cosh \left ( x \right ) +{\it \_C1}\,\sinh \left ( x \right ) }{{x}^{2}}} \right \} \] Mathematica raw input
DSolve[(2 - x^2)*y[x] + 4*x*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> ((2*C[1])/E^x + E^x*C[2])/(2*x^2)}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+4*x*diff(y(x),x)+(-x^2+2)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (_C2*cosh(x)+_C1*sinh(x))/x^2