74.18.28 problem 34

Internal problem ID [16585]
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 : 34
Date solved : Tuesday, January 28, 2025 at 09:11:47 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }+5 y&={\mathrm e}^{t} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 30

dsolve(diff(y(t),t$3)+3*diff(y(t),t$2)-9*diff(y(t),t)+5*y(t)=exp(t),y(t), singsol=all)
 

\[ y = \frac {\left (\left (12 c_{3} t +t^{2}+12 c_{1} \right ) {\mathrm e}^{6 t}+12 c_{2} \right ) {\mathrm e}^{-5 t}}{12} \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 39

DSolve[D[ y[t],{t,3}]+3*D[y[t],{t,2}]-9*D[y[t],t]+5*y[t]==Exp[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^t \left (\frac {t^2}{12}+\left (-\frac {1}{36}+c_3\right ) t+\frac {1}{216}+c_2\right )+c_1 e^{-5 t} \]