68.11.34 problem 46

Internal problem ID [17571]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 46
Date solved : Thursday, October 02, 2025 at 02:25:34 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }&=18 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.022 (sec). Leaf size: 13

ode:=diff(diff(y(t),t),t)+3*diff(y(t),t) = 18; 
ic:=[y(0) = 0, D(y)(0) = 3]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = {\mathrm e}^{-3 t}+6 t -1 \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 15

ode=D[y[t],{t,2}]+3*D[y[t],t]==18; 
ic={y[0]==0,Derivative[1][y][0] ==3}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 6 t+e^{-3 t}-1 \end{align*}

✓ Sympy. Time used: 0.097 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(3*Derivative(y(t), t) + Derivative(y(t), (t, 2)) - 18,0) 
ics = {y(0): 0, Subs(Derivative(y(t), t), t, 0): 3} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 6 t - 1 + e^{- 3 t} \]