Internal problem ID [8685]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1105.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+a y^{\prime }+b x y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 45
dsolve(x*diff(diff(y(x),x),x)+a*diff(y(x),x)+b*x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{-\frac {a}{2}+\frac {1}{2}} \BesselJ \left (\frac {a}{2}-\frac {1}{2}, \sqrt {b}\, x \right )+c_{2} x^{-\frac {a}{2}+\frac {1}{2}} \BesselY \left (\frac {a}{2}-\frac {1}{2}, \sqrt {b}\, x \right ) \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 54
DSolve[b*x*y[x] + a*y'[x] + x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^{\frac {1}{2}-\frac {a}{2}} \left (c_1 J_{\frac {a-1}{2}}\left (\sqrt {b} x\right )+c_2 Y_{\frac {a-1}{2}}\left (\sqrt {b} x\right )\right ) \\ \end{align*}