4.31.4 \(x^2 y''(x)+(x+3) x y'(x)-y(x)=0\)

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 = 0.0254063 (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 = 0.144 (sec), leaf count = 93

\[ \left \{ y \left ( x \right ) =-{1{{\rm e}^{-{\frac {x}{2}}}} \left ( -{\it \_C1}\, \left ( \sqrt {2}+x+1 \right ) {{\sl I}_{-{\frac {1}{2}}+\sqrt {2}}\left ({\frac {x}{2}}\right )}-{\it \_C1}\, \left ( x-\sqrt {2}+1 \right ) {{\sl I}_{{\frac {1}{2}}+\sqrt {2}}\left ({\frac {x}{2}}\right )}+ \left ( \left ( -\sqrt {2}-x-1 \right ) {{\sl K}_{-{\frac {1}{2}}+\sqrt {2}}\left ({\frac {x}{2}}\right )}+{{\sl K}_{{\frac {1}{2}}+\sqrt {2}}\left ({\frac {x}{2}}\right )} \left ( x-\sqrt {2}+1 \right ) \right ) {\it \_C2} \right ) {\frac {1}{\sqrt {x}}}} \right \} \] 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),'implicit')

Maple raw output

y(x) = -exp(-1/2*x)*(-_C1*(2^(1/2)+x+1)*BesselI(-1/2+2^(1/2),1/2*x)-_C1*(x-2^(1/
2)+1)*BesselI(1/2+2^(1/2),1/2*x)+((-2^(1/2)-x-1)*BesselK(-1/2+2^(1/2),1/2*x)+Bes
selK(1/2+2^(1/2),1/2*x)*(x-2^(1/2)+1))*_C2)/x^(1/2)