74.18.26 problem 32

Internal problem ID [16583]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 32
Date solved : Tuesday, January 28, 2025 at 09:11:44 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y^{\prime }+20 y&=-2 t \,{\mathrm e}^{t} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 27

dsolve(diff(y(t),t$2)+9*diff(y(t),t)+20*y(t)=-2*t*exp(t),y(t), singsol=all)
 

\[ y = -\frac {{\mathrm e}^{-5 t} \left (\left (t -\frac {11}{30}\right ) {\mathrm e}^{6 t}-15 c_{2} {\mathrm e}^{t}-15 c_{1} \right )}{15} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 34

DSolve[D[y[t],{t,2}]+9*D[y[t],t]+20*y[t]==-2*t*Exp[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{450} e^t (11-30 t)+c_1 e^{-5 t}+c_2 e^{-4 t} \]