65.6.13 problem 12.1 (xiii)

Internal problem ID [13762]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 12, Homogeneous second order linear equations. Exercises page 118
Problem number : 12.1 (xiii)
Date solved : Tuesday, January 28, 2025 at 06:02:15 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=10\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 17

dsolve([diff(y(t),t$2)-4*y(t)=0,y(0) = 10, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = 5 \,{\mathrm e}^{2 t}+5 \,{\mathrm e}^{-2 t} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 19

DSolve[{D[y[t],{t,2}]-4*y[t]==0,{y[0]==10,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 5 e^{-2 t} \left (e^{4 t}+1\right ) \]