ODE
\[ x^2 y''(x)+x y'(x)-y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00764287 (sec), leaf count = 32
\[\left \{\left \{y(x)\to \frac {c_1 \left (x^2+1\right )+i c_2 \left (x^2-1\right )}{2 x}\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 15
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C2}\,{x}^{2}+{\it \_C1}}{x}} \right \} \] Mathematica raw input
DSolve[-y[x] + x*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> ((1 + x^2)*C[1] + I*(-1 + x^2)*C[2])/(2*x)}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)-y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (_C2*x^2+_C1)/x