8.4.13 problem 13

Internal problem ID [716]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 13
Date solved : Monday, January 27, 2025 at 02:59:05 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: 0.007 (sec). Leaf size: 15

dsolve([y(x)+diff(y(x),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: 0.037 (sec). Leaf size: 21

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

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