66.6.7 problem 7

Internal problem ID [16019]
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 : 7
Date solved : Thursday, October 02, 2025 at 10:38:56 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.026 (sec). Leaf size: 17

ode:=diff(y(t),t)+2*y(t) = exp(1/3*t); 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \frac {3 \,{\mathrm e}^{\frac {t}{3}}}{7}+\frac {4 \,{\mathrm e}^{-2 t}}{7} \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 25

ode=D[y[t],t]+2*y[t]==Exp[t/3]; 
ic={y[0]==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{7} e^{-2 t} \left (3 e^{7 t/3}+4\right ) \end{align*}

✓ Sympy. Time used: 0.086 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(2*y(t) - exp(t/3) + Derivative(y(t), t),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {3 e^{\frac {t}{3}}}{7} + \frac {4 e^{- 2 t}}{7} \]