60.3.97 problem 1101

Internal problem ID [11107]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1101
Date solved : Monday, January 27, 2025 at 10:45:55 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }+2 y^{\prime }+a x y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 29

dsolve(x*diff(diff(y(x),x),x)+2*diff(y(x),x)+y(x)*a*x=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} \sinh \left (\sqrt {-a}\, x \right )+c_{2} \cosh \left (\sqrt {-a}\, x \right )}{x} \]

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 52

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

\[ y(x)\to \frac {2 c_1 e^{-i \sqrt {a} x}-\frac {i c_2 e^{i \sqrt {a} x}}{\sqrt {a}}}{2 x} \]