10.7.17 problem 19

Internal problem ID [1265]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.1 Homogeneous Equations with Constant Coefficients, page 144
Problem number : 19
Date solved : Monday, January 27, 2025 at 04:48:22 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&={\frac {5}{4}}\\ y^{\prime }\left (0\right )&=-{\frac {3}{4}} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 13

dsolve([diff(y(x),x$2) -y(x) = 0,y(0) = 5/4, D(y)(0) = -3/4],y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{x}}{4}+{\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 18

DSolve[{D[y[x],{x,2}]-y[x]==0,{y[0]==5/4,Derivative[1][y][0] ==-3/4}},y[x],x,IncludeSingularSolutions -> True]
 

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