76.13.43 problem 43

Internal problem ID [17625]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 43
Date solved : Tuesday, January 28, 2025 at 10:45:55 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: 0.069 (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)
 

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

✓ Solution by Mathematica

Time used: 0.011 (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]
 

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