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 = 0.023615 (sec), leaf count = 20
\[\left \{\left \{y(x)\to \frac {c_1 x^{5/2}+c_2}{x}\right \}\right \}\]
Maple ✓
cpu = 0.01 (sec), leaf count = 15
\[ \left \{ y \left ( x \right ) ={\frac {1}{x} \left ( {\it \_C1}\,{x}^{{\frac {5}{2}}}+{\it \_C2} \right ) } \right \} \] Mathematica raw input
DSolve[-3*y[x] + x*y'[x] + 2*x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (x^(5/2)*C[1] + 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),'implicit')
Maple raw output
y(x) = (_C1*x^(5/2)+_C2)/x