Internal problem ID [9525]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1195.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+\left (x +3\right ) x y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 93
dsolve(x^2*diff(diff(y(x),x),x)+(x+3)*x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (-c_{1} \left (\sqrt {2}+x +1\right ) \operatorname {BesselI}\left (-\frac {1}{2}+\sqrt {2}, \frac {x}{2}\right )-c_{1} \left (-\sqrt {2}+x +1\right ) \operatorname {BesselI}\left (\frac {1}{2}+\sqrt {2}, \frac {x}{2}\right )+c_{2} \left (\left (-\sqrt {2}-x -1\right ) \operatorname {BesselK}\left (-\frac {1}{2}+\sqrt {2}, \frac {x}{2}\right )+\operatorname {BesselK}\left (\frac {1}{2}+\sqrt {2}, \frac {x}{2}\right ) \left (-\sqrt {2}+x +1\right )\right )\right ) {\mathrm e}^{-\frac {x}{2}}}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 63
DSolve[-y[x] + x*(3 + x)*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} x^{\sqrt {2}-1} \left (c_1 \operatorname {HypergeometricU}\left (2+\sqrt {2},1+2 \sqrt {2},x\right )+c_2 L_{-2-\sqrt {2}}^{2 \sqrt {2}}(x)\right ) \]