72.1.4 problem 7

Internal problem ID [14525]
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 1.2. page 33
Problem number : 7
Date solved : Thursday, March 13, 2025 at 03:32:18 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 12

ode:=diff(y(t),t) = 2*y(t)+1; 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 24

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

\begin{align*} y(t)\to -\frac {1}{2}+c_1 e^{2 t} \\ y(t)\to -\frac {1}{2} \\ \end{align*}

✓ Sympy. Time used: 0.123 (sec). Leaf size: 12

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

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