72.3.1 problem 1

Internal problem ID [14586]
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 : Thursday, March 13, 2025 at 03:37:52 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*}

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

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

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

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

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

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

✓ Sympy. Time used: 0.137 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-2*y(t) + Derivative(y(t), t) - 1,0) 
ics = {y(0): 3} 
dsolve(ode,func=y(t),ics=ics)
 

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