83.9.1 problem 1

Internal problem ID [19159]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter III. Ordinary linear differential equations with constant coefficients. Exercise III(A) at page 31
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 01:10:39 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 23

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

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