ODE
\[ x^2 y''(x)-x y'(x)-3 y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0262405 (sec), leaf count = 18
\[\left \{\left \{y(x)\to \frac {c_1 x^4+c_2}{x}\right \}\right \}\]
Maple ✓
cpu = 0.01 (sec), leaf count = 15
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\,{x}^{4}+{\it \_C2}}{x}} \right \} \] Mathematica raw input
DSolve[-3*y[x] - x*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (x^4*C[1] + C[2])/x}}
Maple raw input
dsolve(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^4+_C2)/x