83.29.3 problem 3

Internal problem ID [19376]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (C) at page 107
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 01:35:47 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

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

\[ y \left (x \right ) = {\mathrm e}^{a x} c_{1} +{\mathrm e}^{-a x} c_{2} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 23

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

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