90.4.16 problem 17

Internal problem ID [25111]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 59
Problem number : 17
Date solved : Thursday, October 02, 2025 at 11:50:28 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 22

ode:=diff(y(t),t)+a*y(t) = exp(b*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{-a t} c_1 +\frac {{\mathrm e}^{b t}}{a +b} \]

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 31

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

\begin{align*} y(t)&\to \frac {e^{-a t} \left (e^{t (a+b)}+c_1 (a+b)\right )}{a+b} \end{align*}

✓ Sympy. Time used: 0.083 (sec). Leaf size: 17

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

\[ y{\left (t \right )} = C_{1} e^{- a t} + \frac {e^{b t}}{a + b} \]