74.12.2 problem 2

Internal problem ID [16309]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 09:02:35 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+16 y^{\prime }&=t \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

dsolve(diff(y(t),t$2)+16*diff(y(t),t)=t,y(t), singsol=all)
 

\[ y = \frac {t^{2}}{32}-\frac {{\mathrm e}^{-16 t} c_{1}}{16}-\frac {t}{256}+c_{2} \]

✓ Solution by Mathematica

Time used: 4.794 (sec). Leaf size: 42

DSolve[D[y[t],{t,2}]+16*D[y[t],t]==t,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \int _1^te^{-16 K[2]} \left (c_1+\int _1^{K[2]}e^{16 K[1]} K[1]dK[1]\right )dK[2]+c_2 \]