72.3.1 problem 1

Internal problem ID [14665]
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 1.4 page 61
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 06:46:52 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=2 y+1 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 12

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

\[ y = -\frac {1}{2}+\frac {7 \,{\mathrm e}^{2 t}}{2} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 18

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

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