ODE
\[ x^2 y''(x)+(x+3) x y'(x)-y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.168829 (sec), leaf count = 63
\[\left \{\left \{y(x)\to e^{-x} x^{\sqrt {2}-1} \left (c_1 U\left (2+\sqrt {2},1+2 \sqrt {2},x\right )+c_2 L_{-2-\sqrt {2}}^{2 \sqrt {2}}(x)\right )\right \}\right \}\]
Maple ✓
cpu = 0.43 (sec), leaf count = 94
\[\left [y \left (x \right ) = \frac {\textit {\_C1} \,{\mathrm e}^{-\frac {x}{2}} \left (\left (\sqrt {2}+x +1\right ) \BesselI \left (-\frac {1}{2}+\sqrt {2}, \frac {x}{2}\right )+\left (-\sqrt {2}+x +1\right ) \BesselI \left (\frac {1}{2}+\sqrt {2}, \frac {x}{2}\right )\right )}{\sqrt {x}}+\frac {\textit {\_C2} \left (\left (\sqrt {2}+x +1\right ) \BesselK \left (-\frac {1}{2}+\sqrt {2}, \frac {x}{2}\right )-\BesselK \left (\frac {1}{2}+\sqrt {2}, \frac {x}{2}\right ) \left (-\sqrt {2}+x +1\right )\right ) {\mathrm e}^{-\frac {x}{2}}}{\sqrt {x}}\right ]\] Mathematica raw input
DSolve[-y[x] + x*(3 + x)*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (x^(-1 + Sqrt[2])*(C[1]*HypergeometricU[2 + Sqrt[2], 1 + 2*Sqrt[2], x] + C[2]*LaguerreL[-2 - Sqrt[2], 2*Sqrt[2], x]))/E^x}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+x*(3+x)*diff(y(x),x)-y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*exp(-1/2*x)/x^(1/2)*((2^(1/2)+x+1)*BesselI(-1/2+2^(1/2),1/2*x)+(-2^(1/2)+x+1)*BesselI(1/2+2^(1/2),1/2*x))+_C2/x^(1/2)*((2^(1/2)+x+1)*BesselK(-1/2+2^(1/2),1/2*x)-BesselK(1/2+2^(1/2),1/2*x)*(-2^(1/2)+x+1))*exp(-1/2*x)]