Internal problem ID [14571]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number: 62 (d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+4 y={\mathrm e}^{-4 t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve([diff(y(t),t)+4*y(t)=exp(-4*t),y(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \left (t +1\right ) {\mathrm e}^{-4 t} \]
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 14
DSolve[{y'[t]+4*y[t]==Exp[-4*t],{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-4 t} (t+1) \]