82.54.1 problem Ex. 1

Internal problem ID [19017]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IX. Equations of the second order. problems at end of chapter at page 120
Problem number : Ex. 1
Date solved : Tuesday, January 28, 2025 at 12:45:48 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}&=n^{2} y \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 21

dsolve(diff(y(x),x$2)+2/x*diff(y(x),x)=n^2*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {c_{1} \sinh \left (n x \right )+c_{2} \cosh \left (n x \right )}{x} \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 35

DSolve[D[y[x],{x,2}]+2/x*D[y[x],x]==n^2*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2 c_1 n e^{-n x}+c_2 e^{n x}}{2 n x} \]