72.6.11 problem 11

Internal problem ID [14665]
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 : 11
Date solved : Monday, March 31, 2025 at 12:52:02 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-2 y&=7 \,{\mathrm e}^{2 t} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3 \end{align*}

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

ode:=diff(y(t),t)-2*y(t) = 7*exp(2*t); 
ic:=y(0) = 3; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \left (7 t +3\right ) {\mathrm e}^{2 t} \]

✓ Mathematica. Time used: 0.042 (sec). Leaf size: 16

ode=D[y[t],t]-2*y[t]==7*Exp[2*t]; 
ic={y[0]==3}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{2 t} (7 t+3) \]

✓ Sympy. Time used: 0.155 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-2*y(t) - 7*exp(2*t) + Derivative(y(t), t),0) 
ics = {y(0): 3} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (7 t + 3\right ) e^{2 t} \]