72.6.8 problem 8

Internal problem ID [14662]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.8 page 121
Problem number : 8
Date solved : Monday, March 31, 2025 at 12:51:54 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-2 y&=3 \,{\mathrm e}^{-2 t} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=10 \end{align*}

✓ Maple. Time used: 0.028 (sec). Leaf size: 17

ode:=diff(y(t),t)-2*y(t) = 3*exp(-2*t); 
ic:=y(0) = 10; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \frac {43 \,{\mathrm e}^{2 t}}{4}-\frac {3 \,{\mathrm e}^{-2 t}}{4} \]

✓ Mathematica. Time used: 0.063 (sec). Leaf size: 23

ode=D[y[t],t]-2*y[t]==3*Exp[-2*t]; 
ic={y[0]==10}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {1}{4} e^{-2 t} \left (43 e^{4 t}-3\right ) \]

✓ Sympy. Time used: 0.155 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-2*y(t) + Derivative(y(t), t) - 3*exp(-2*t),0) 
ics = {y(0): 10} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {43 e^{2 t}}{4} - \frac {3 e^{- 2 t}}{4} \]