60.3.101 problem 1105

Internal problem ID [11111]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1105
Date solved : Monday, January 27, 2025 at 10:46:02 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }+a y^{\prime }+b x y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 39

dsolve(x*diff(diff(y(x),x),x)+a*diff(y(x),x)+b*x*y(x)=0,y(x), singsol=all)
 

\[ y = \left (\operatorname {BesselJ}\left (\frac {a}{2}-\frac {1}{2}, \sqrt {b}\, x \right ) c_{1} +\operatorname {BesselY}\left (\frac {a}{2}-\frac {1}{2}, \sqrt {b}\, x \right ) c_{2} \right ) x^{-\frac {a}{2}+\frac {1}{2}} \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 54

DSolve[b*x*y[x] + a*D[y[x],x] + x*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^{\frac {1}{2}-\frac {a}{2}} \left (c_1 \operatorname {BesselJ}\left (\frac {a-1}{2},\sqrt {b} x\right )+c_2 \operatorname {BesselY}\left (\frac {a-1}{2},\sqrt {b} x\right )\right ) \]