74.5.44 problem 51

Internal problem ID [15937]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 51
Date solved : Monday, March 31, 2025 at 02:13:55 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-5 y&=t \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

ode:=diff(y(t),t)-5*y(t) = t; 
dsolve(ode,y(t), singsol=all);
 

\[ y = -\frac {t}{5}-\frac {1}{25}+{\mathrm e}^{5 t} c_1 \]

✓ Mathematica. Time used: 0.057 (sec). Leaf size: 30

ode=D[y[t],t]-5*y[t]==t; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{5 t} \left (\int _1^te^{-5 K[1]} K[1]dK[1]+c_1\right ) \]

✓ Sympy. Time used: 0.129 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t - 5*y(t) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{5 t} - \frac {t}{5} - \frac {1}{25} \]