71.4.14 problem 14

Internal problem ID [14386]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 06:29:16 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }+3 y&=1 \end{align*}

With initial conditions

\begin{align*} y \left (-2\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 14

dsolve([diff(y(x),x)+3*y(x)=1,y(-2) = 1],y(x), singsol=all)
 

\[ y = \frac {1}{3}+\frac {2 \,{\mathrm e}^{-6-3 x}}{3} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 20

DSolve[{D[y[x],x]+3*y[x]==1,{y[-2]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2}{3} e^{-3 (x+2)}+\frac {1}{3} \]