90.1.21 problem 32

Internal problem ID [25045]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 13
Problem number : 32
Date solved : Thursday, October 02, 2025 at 11:47:48 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=3 y+12 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-2 \\ \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 12

ode:=diff(y(t),t) = 3*y(t)+12; 
ic:=[y(0) = -2]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = -4+2 \,{\mathrm e}^{3 t} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 14

ode=D[y[t],{t,1}]== 3*y[t]+12; 
ic={y[0]==-2}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 2 \left (e^{3 t}-2\right ) \end{align*}

✓ Sympy. Time used: 0.080 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-3*y(t) + Derivative(y(t), t) - 12,0) 
ics = {y(0): -2} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 2 e^{3 t} - 4 \]