ODE
\[ -\left (4-x^2\right ) y'(x)+x y''(x)+2 x y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0261531 (sec), leaf count = 68
\[\left \{\left \{y(x)\to \frac {1}{30} \left (\sqrt {2 \pi } c_2 e^{-\frac {x^2}{2}} x^5 \text {erfi}\left (\frac {x}{\sqrt {2}}\right )+30 c_1 e^{-\frac {x^2}{2}} x^5-2 c_2 \left (x^4+x^2+3\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.055 (sec), leaf count = 46
\[ \left \{ y \left ( x \right ) ={x}^{5} \left ( i{\it \_C2}\,\sqrt {2}\sqrt {\pi }{\it Erf} \left ( {\frac {i}{2}}\sqrt {2}x \right ) +{\it \_C1} \right ) {{\rm e}^{-{\frac {{x}^{2}}{2}}}}+2\,{\it \_C2}\, \left ( {x}^{4}+{x}^{2}+3 \right ) \right \} \] Mathematica raw input
DSolve[2*x*y[x] - (4 - x^2)*y'[x] + x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> ((30*x^5*C[1])/E^(x^2/2) - 2*(3 + x^2 + x^4)*C[2] + (Sqrt[2*Pi]*x^5*C[2]*Erfi[x/Sqrt[2]])/E^(x^2/2))/30}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x)-(-x^2+4)*diff(y(x),x)+2*x*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = x^5*(I*_C2*2^(1/2)*Pi^(1/2)*erf(1/2*I*2^(1/2)*x)+_C1)*exp(-1/2*x^2)+2*_C2*(x^4+x^2+3)