ODE
\[ x^2 y'(x)+y''(x)-4 x y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.417769 (sec), leaf count = 69
\[\left \{\left \{y(x)\to \frac {1}{36} \left (36 c_1 x \left (x^3+4\right )-3 c_2 e^{-\frac {x^3}{3}} \left (x^3+3\right )+3^{2/3} c_2 \sqrt [3]{x^3} \left (x^3+4\right ) \Gamma \left (\frac {2}{3},\frac {x^3}{3}\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.566 (sec), leaf count = 31
\[\left [y \left (x \right ) = \textit {\_C1} x \left (x^{3}+4\right )+\textit {\_C2} \,{\mathrm e}^{-\frac {x^{3}}{3}} \hypergeom \left (\left [2\right ], \left [\frac {2}{3}\right ], \frac {x^{3}}{3}\right )\right ]\] Mathematica raw input
DSolve[-4*x*y[x] + x^2*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (36*x*(4 + x^3)*C[1] - (3*(3 + x^3)*C[2])/E^(x^3/3) + 3^(2/3)*(x^3)^(1/3)*(4 + x^3)*C[2]*Gamma[2/3, x^3/3])/36}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+x^2*diff(y(x),x)-4*x*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x*(x^3+4)+_C2*exp(-1/3*x^3)*hypergeom([2],[2/3],1/3*x^3)]