74.11.31 problem 43

Internal problem ID [16281]
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 : 43
Date solved : Tuesday, January 28, 2025 at 09:00:17 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }&=-24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 26

dsolve(diff(y(t),t$2)+4*diff(y(t),t)=-24*t-6-4*t*exp(-4*t)+exp(-4*t),y(t), singsol=all)
 

\[ y = \frac {\left (2 t^{2}-c_{1} \right ) {\mathrm e}^{-4 t}}{4}-3 t^{2}+c_{2} \]

✓ Solution by Mathematica

Time used: 4.469 (sec). Leaf size: 75

DSolve[D[y[t],{t,2}]+4*D[y[t],t]==-24*t-6-4*t*Exp[-4*t]+Exp[-4*t],y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \int _1^te^{-4 K[1]} \left (c_1-K[1] \left (2 K[1]+6 e^{4 K[1]}-1\right )\right )dK[1]+c_2 \\ y(t)\to \frac {1}{2} e^{-4 t} t^2-3 t^2-\frac {1}{2 e^4}+3+c_2 \\ \end{align*}