74.14.20 problem 20

Internal problem ID [16425]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.6, page 187
Problem number : 20
Date solved : Tuesday, January 28, 2025 at 09:07:49 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }-11 y^{\prime }+30 y&={\mathrm e}^{4 t} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 34

dsolve(diff(y(t),t$3)-4*diff(y(t),t$2)-11*diff(y(t),t)+30*y(t)=exp(4*t),y(t), singsol=all)
 

\[ y = \frac {\left (14 c_{3} {\mathrm e}^{8 t}-{\mathrm e}^{7 t}+14 c_{2} {\mathrm e}^{5 t}+14 c_{1} \right ) {\mathrm e}^{-3 t}}{14} \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 39

DSolve[D[ y[t],{t,3}]-4*D[y[t],{t,2}]-11*D[y[t],t]+30*y[t]==Exp[4*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {e^{4 t}}{14}+c_1 e^{-3 t}+c_2 e^{2 t}+c_3 e^{5 t} \]