83.37.2 problem 2

Internal problem ID [19447]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VIII. Linear equations of second order. Excercise VIII (B) at page 128
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 01:43:06 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 42

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

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