72.6.7 problem 7

Internal problem ID [14732]
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 : Tuesday, January 28, 2025 at 07:13:03 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*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 25

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

\[ y(t)\to \frac {1}{7} e^{-2 t} \left (3 e^{7 t/3}+4\right ) \]