74.11.34 problem 46

Internal problem ID [16284]
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 : Tuesday, January 28, 2025 at 09:00:25 AM
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*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 13

dsolve([diff(y(t),t$2)+3*diff(y(t),t)=18,y(0) = 0, D(y)(0) = 3],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 15

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

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