7.8.8 problem 8

Internal problem ID [222]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.1 (Introduction. Second order linear equations). Problems at page 111
Problem number : 8
Date solved : Wednesday, February 05, 2025 at 03:06:08 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 12

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

\[ y = \frac {14}{3}-\frac {2 \,{\mathrm e}^{3 x}}{3} \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 14

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

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