69.1.84 problem 129

Internal problem ID [14237]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 129
Date solved : Tuesday, January 28, 2025 at 06:22:59 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }&=9 y \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(diff(y(x),x$2)=9*y(x),y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{-3 x}+{\mathrm e}^{3 x} c_{2} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 22

DSolve[D[y[x],{x,2}]==9*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} \left (c_1 e^{6 x}+c_2\right ) \]