72.6.11 problem 11

Internal problem ID [14736]
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 : Tuesday, January 28, 2025 at 07:13:11 AM
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*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

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

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

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