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 = 0.213391 (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 = 0.083 (sec), leaf count = 32
\[\left [y \left (x \right ) = \textit {\_C1} x \,{\mathrm e}^{\frac {1}{2 x^{2}}}+\textit {\_C2} x \,{\mathrm e}^{\frac {1}{2 x^{2}}} \erf \left (\frac {\sqrt {2}}{2 x}\right )\right ]\] 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))
Maple raw output
[y(x) = _C1*x*exp(1/2/x^2)+_C2*x*exp(1/2/x^2)*erf(1/2*2^(1/2)/x)]