74.11.52 problem 62 (c)

Internal problem ID [16302]
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 (c)
Date solved : Tuesday, January 28, 2025 at 09:02:10 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-y&={\mathrm e}^{4 t} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 14

dsolve([diff(y(t),t)-y(t)=exp(4*t),y(0) = 0],y(t), singsol=all)
 

\[ y = \frac {\left ({\mathrm e}^{3 t}-1\right ) {\mathrm e}^{t}}{3} \]

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 19

DSolve[{D[y[t],t]-y[t]==Exp[4*t],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{3} e^t \left (e^{3 t}-1\right ) \]