ODE
\[ 2 x^2 y''(x)+x y'(x)-3 y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.156325 (sec), leaf count = 20
\[\left \{\left \{y(x)\to \frac {c_2 x^{5/2}+c_1}{x}\right \}\right \}\]
Maple ✓
cpu = 0.014 (sec), leaf count = 15
\[\left [y \left (x \right ) = \frac {\textit {\_C1}}{x}+\textit {\_C2} \,x^{\frac {3}{2}}\right ]\] Mathematica raw input
DSolve[-3*y[x] + x*y'[x] + 2*x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[1] + x^(5/2)*C[2])/x}}
Maple raw input
dsolve(2*x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)-3*y(x) = 0, y(x))
Maple raw output
[y(x) = 1/x*_C1+_C2*x^(3/2)]