72.8.19 problem 32

Internal problem ID [14712]
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. Review Exercises for chapter 1. page 136
Problem number : 32
Date solved : Monday, March 31, 2025 at 12:54:55 PM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=-1 \end{align*}

✓ Maple. Time used: 0.028 (sec). Leaf size: 14

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

\[ y = \left (2 t -1\right ) {\mathrm e}^{3 t} \]

✓ Mathematica. Time used: 0.042 (sec). Leaf size: 16

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

\[ y(t)\to e^{3 t} (2 t-1) \]

✓ Sympy. Time used: 0.140 (sec). Leaf size: 12

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

\[ y{\left (t \right )} = \left (2 t - 1\right ) e^{3 t} \]