72.6.8 problem 8

Internal problem ID [14733]
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 : Tuesday, January 28, 2025 at 07:13:05 AM
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*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

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

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

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