ODE
\[ x^4 y''(x)+x y'(x)-2 y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0398255 (sec), leaf count = 45
\[\left \{\left \{y(x)\to \frac {1}{2} e^{\frac {1}{2 x^2}} x \left (2 c_1-\sqrt {2 \pi } c_2 \text {erf}\left (\frac {1}{\sqrt {2} x}\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.069 (sec), leaf count = 25
\[ \left \{ y \left ( x \right ) =x{{\rm e}^{{\frac {1}{2\,{x}^{2}}}}} \left ( {\it Erf} \left ( {\frac {\sqrt {2}}{2\,x}} \right ) {\it \_C2}+{\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[-2*y[x] + x*y'[x] + x^4*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (E^(1/(2*x^2))*x*(2*C[1] - Sqrt[2*Pi]*C[2]*Erf[1/(Sqrt[2]*x)]))/2}}
Maple raw input
dsolve(x^4*diff(diff(y(x),x),x)+x*diff(y(x),x)-2*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = x*exp(1/2/x^2)*(erf(1/2*2^(1/2)/x)*_C2+_C1)