Internal problem ID [4459]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 2, First order differential equations. Section 2.3, Linear equations. Exercises. page
54
Problem number: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }+4 y-{\mathrm e}^{-x}=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = {\frac {4}{3}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve([diff(y(x),x)+4*y(x)-exp(-x)=0,y(0) = 4/3],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left ({\mathrm e}^{3 x}+3\right ) {\mathrm e}^{-4 x}}{3} \]
✓ Solution by Mathematica
Time used: 0.086 (sec). Leaf size: 21
DSolve[{y'[x]+4*y[x]-Exp[-x]==0,{y[0]==4/3}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} e^{-4 x} \left (e^{3 x}+3\right ) \\ \end{align*}