Internal problem ID [8884]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1305.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{3} y^{\prime \prime }+2 y^{\prime } x -y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 49
dsolve(x^3*diff(diff(y(x),x),x)+2*x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\frac {1}{x}} \left (\BesselI \left (0, -\frac {1}{x}\right )+\BesselI \left (1, -\frac {1}{x}\right )\right )+c_{2} {\mathrm e}^{\frac {1}{x}} \left (\BesselK \left (0, -\frac {1}{x}\right )-\BesselK \left (1, -\frac {1}{x}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 47
DSolve[-y[x] + 2*x*y'[x] + x^3*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 G_{1,2}^{2,0}\left (-\frac {2}{x}| {c} \frac {1}{2} \\ -1,0 \\ \\ \right )+c_1 e^{\frac {1}{x}} \left (I_0\left (\frac {1}{x}\right )-I_1\left (\frac {1}{x}\right )\right ) \\ \end{align*}