74.5.48 problem 55

Internal problem ID [15941]
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 : 55
Date solved : Monday, March 31, 2025 at 02:14:04 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+10 y&=2 \,{\mathrm e}^{t} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=diff(y(t),t)+10*y(t) = 2*exp(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {2 \,{\mathrm e}^{t}}{11}+{\mathrm e}^{-10 t} c_1 \]

✓ Mathematica. Time used: 0.055 (sec). Leaf size: 21

ode=D[y[t],t]+10*y[t]==2*Exp[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {2 e^t}{11}+c_1 e^{-10 t} \]

✓ Sympy. Time used: 0.131 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(10*y(t) - 2*exp(t) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- 10 t} + \frac {2 e^{t}}{11} \]