68.11.52 problem 62 (c)

Internal problem ID [17589]
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 : Thursday, October 02, 2025 at 02:25:56 PM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Maple. Time used: 0.030 (sec). Leaf size: 15

ode:=diff(y(t),t)-y(t) = exp(4*t); 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = -\frac {{\mathrm e}^{t}}{3}+\frac {{\mathrm e}^{4 t}}{3} \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 19

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

\begin{align*} y(t)&\to \frac {1}{3} e^t \left (e^{3 t}-1\right ) \end{align*}

✓ Sympy. Time used: 0.082 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-y(t) - exp(4*t) + Derivative(y(t), t),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

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