10.7.16 problem 16

Internal problem ID [1264]
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 : 16
Date solved : Monday, January 27, 2025 at 04:48:19 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (-2\right )&=1\\ y^{\prime }\left (-2\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 25

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

\[ y(x)\to -\frac {1}{2} e^{-\frac {x}{2}-1} \left (e^{x+2}-3\right ) \]