69.1.75 problem 120

Internal problem ID [14149]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 120
Date solved : Wednesday, March 05, 2025 at 10:36:49 PM
CAS classification : [[_2nd_order, _missing_x]]

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

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

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

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 23

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

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

✓ Sympy. Time used: 0.083 (sec). Leaf size: 15

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

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