8.4.1 problem 1

Internal problem ID [704]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 1
Date solved : Wednesday, February 05, 2025 at 03:51:18 AM
CAS classification : [_quadrature]

\begin{align*} y+y^{\prime }&=2 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 12

dsolve([y(x)+diff(y(x),x) = 2,y(0) = 0],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 14

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

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