ODE
\[ x^3 y''(x)+x y'(x)-y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.193525 (sec), leaf count = 18
\[\left \{\left \{y(x)\to x \left (c_1 e^{\frac {1}{x}}+c_2\right )\right \}\right \}\]
Maple ✓
cpu = 0.041 (sec), leaf count = 15
\[\left [y \left (x \right ) = {\mathrm e}^{\frac {1}{x}} x \textit {\_C1} +\textit {\_C2} x\right ]\] Mathematica raw input
DSolve[-y[x] + x*y'[x] + x^3*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*(E^x^(-1)*C[1] + C[2])}}
Maple raw input
dsolve(x^3*diff(diff(y(x),x),x)+x*diff(y(x),x)-y(x) = 0, y(x))
Maple raw output
[y(x) = exp(1/x)*x*_C1+_C2*x]