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 = 1.42298 (sec), leaf count = 87
\[\left \{\left \{y(x)\to \frac {1}{36} e^{-\frac {x^3}{3}} \left (36 c_1 e^{\frac {x^3}{3}} x \left (x^3+4\right )-3 c_2 \left (x^3+3\right )+3^{2/3} c_2 e^{\frac {x^3}{3}} \sqrt [3]{x^3} \left (x^3+4\right ) \Gamma \left (\frac {2}{3},\frac {x^3}{3}\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.23 (sec), leaf count = 31
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,x \left ( {x}^{3}+4 \right ) +{\it \_C2}\,{{\rm e}^{-{\frac {{x}^{3}}{3}}}}{\mbox {$_1$F$_1$}(2;\,{\frac {2}{3}};\,{\frac {{x}^{3}}{3}})} \right \} \] Mathematica raw input
DSolve[-4*x*y[x] + x^2*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (36*E^(x^3/3)*x*(4 + x^3)*C[1] - 3*(3 + x^3)*C[2] + 3^(2/3)*E^(x^3/3)*(x^3)^(1/3)*(4 + x^3)*C[2]*Gamma[2/3, x^3/3])/(36*E^(x^3/3))}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+x^2*diff(y(x),x)-4*x*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*x*(x^3+4)+_C2*exp(-1/3*x^3)*hypergeom([2],[2/3],1/3*x^3)