7.4.13 problem 13

Internal problem ID [85]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.5 (linear equations). Problems at page 54
Problem number : 13
Date solved : Friday, February 07, 2025 at 07:48:50 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&={\mathrm e}^{x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 15

dsolve([diff(y(x),x)+y(x)=exp(x),y(0) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 21

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

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