ODE
\[ x^2 y''(x)=2 y(x) \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.016399 (sec), leaf count = 18
\[\left \{\left \{y(x)\to \frac {c_1 x^3+c_2}{x}\right \}\right \}\]
Maple ✓
cpu = 0.009 (sec), leaf count = 15
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C2}\,{x}^{3}+{\it \_C1}}{x}} \right \} \] Mathematica raw input
DSolve[x^2*y''[x] == 2*y[x],y[x],x]
Mathematica raw output
{{y[x] -> (x^3*C[1] + C[2])/x}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x) = 2*y(x), y(x),'implicit')
Maple raw output
y(x) = (_C2*x^3+_C1)/x