ODE
\[ x^2 y''(x)=2 y(x) \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.162218 (sec), leaf count = 18
\[\left \{\left \{y(x)\to \frac {c_2 x^3+c_1}{x}\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 15
\[\left [y \left (x \right ) = \frac {\textit {\_C1}}{x}+\textit {\_C2} \,x^{2}\right ]\] Mathematica raw input
DSolve[x^2*y''[x] == 2*y[x],y[x],x]
Mathematica raw output
{{y[x] -> (C[1] + x^3*C[2])/x}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x) = 2*y(x), y(x))
Maple raw output
[y(x) = 1/x*_C1+_C2*x^2]