86.3.6 problem 5 (ii)

Internal problem ID [23097]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 4. Linear equations of the first order. Exercise 4a at page 56
Problem number : 5 (ii)
Date solved : Thursday, October 02, 2025 at 09:20:08 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-6 y&={\mathrm e}^{6 t} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 12

ode:=diff(y(t),t)-6*y(t) = exp(6*t); 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \left (t +1\right ) {\mathrm e}^{6 t} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 14

ode=D[y[t],t]-6*y[t]==Exp[6*t]; 
ic={y[0]==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{6 t} (t+1) \end{align*}

✓ Sympy. Time used: 0.097 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-6*y(t) - exp(6*t) + Derivative(y(t), t),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (t + 1\right ) e^{6 t} \]