69.1.75 problem 120

Internal problem ID [14228]
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 : Tuesday, January 28, 2025 at 06:22:39 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

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