74.11.19 problem 31

Internal problem ID [16269]
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 : 31
Date solved : Tuesday, January 28, 2025 at 08:59:42 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 8 y^{\prime \prime }+6 y^{\prime }+y&=5 t^{2} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 27

dsolve(8*diff(y(t),t$2)+6*diff(y(t),t)+y(t)=5*t^2,y(t), singsol=all)
 

\[ y = -4 \,{\mathrm e}^{-\frac {t}{2}} c_{1} +{\mathrm e}^{-\frac {t}{4}} c_{2} +5 t^{2}-60 t +280 \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 35

DSolve[8*D[y[t],{t,2}]+6*D[y[t],t]+y[t]==5*t^2,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 5 t^2-60 t+c_1 e^{-t/4}+c_2 e^{-t/2}+280 \]