76.2.5 problem 5

Internal problem ID [17341]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.2 (Linear equations: Method of integrating factors). Problems at page 54
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 10:01:46 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

dsolve(diff(y(t),t)-2*y(t)=3*exp(t),y(t), singsol=all)
 

\[ y = -3 \,{\mathrm e}^{t}+c_{1} {\mathrm e}^{2 t} \]

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 17

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

\[ y(t)\to e^t \left (-3+c_1 e^t\right ) \]