82.54.3 problem Ex. 3

Internal problem ID [19019]
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. 3
Date solved : Tuesday, January 28, 2025 at 12:45:53 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\left (n^{2}+\frac {2}{x^{2}}\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)-2/x*diff(y(x),x)+(n^2+2/x^2)*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = x \left (c_{1} \sin \left (n x \right )+c_{2} \cos \left (n x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 38

DSolve[D[y[x],{x,2}]-2/x*D[y[x],x]+(n^2+2/x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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