77.9.1 problem 1

Internal problem ID [20444]
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 : Thursday, October 02, 2025 at 06:02:57 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

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

\[ y = c_1 \,{\mathrm e}^{n x}+c_2 \,{\mathrm e}^{-n x} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 23

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

\begin{align*} y(x)&\to c_1 e^{n x}+c_2 e^{-n x} \end{align*}

✓ Sympy. Time used: 0.044 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
n = symbols("n") 
y = Function("y") 
ode = Eq(-n**2*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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