78.10.8 problem 6 (d)

Internal problem ID [18269]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 15. The General Solution of the Homogeneous Equation. Problems at page 117
Problem number : 6 (d)
Date solved : Tuesday, January 28, 2025 at 11:44:55 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (2\right )&=0\\ y^{\prime }\left (2\right )&={\mathrm e}^{-2} \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 13

dsolve([diff(y(x),x$2)+diff(y(x),x)=0,y(2) = 0, D(y)(2) = exp(-2)],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 16

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

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