74.13.35 problem 59

Internal problem ID [16401]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.5, page 175
Problem number : 59
Date solved : Tuesday, January 28, 2025 at 09:07:30 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+12 y^{\prime \prime \prime }+60 y^{\prime \prime }+124 y^{\prime }+75 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 37

dsolve(diff(y(t),t$4)+12*diff(y(t),t$3)+60*diff(y(t),t$2)+124*diff(y(t),t)+75*y(t)=0,y(t), singsol=all)
 

\[ y = {\mathrm e}^{-3 t} c_{1} +c_{2} {\mathrm e}^{-t}+c_{3} {\mathrm e}^{-4 t} \sin \left (3 t \right )+c_4 \,{\mathrm e}^{-4 t} \cos \left (3 t \right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 40

DSolve[D[y[t],{t,4}]+12*D[ y[t],{t,3}]+60*D[y[t],{t,2}]+124*D[y[t],t]+75*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-4 t} \left (c_3 e^t+c_4 e^{3 t}+c_2 \cos (3 t)+c_1 \sin (3 t)\right ) \]