73.10.14 problem 15.6 (a)

Internal problem ID [15309]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 15. General solutions to Homogeneous linear differential equations. Additional exercises page 294
Problem number : 15.6 (a)
Date solved : Tuesday, January 28, 2025 at 07:52:07 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 )&=1\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

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

dsolve([diff(y(x),x$2)-4*y(x)=0,y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{2 x}}{2}+\frac {{\mathrm e}^{-2 x}}{2} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 21

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

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