74.13.30 problem 47

Internal problem ID [16396]
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 : 47
Date solved : Tuesday, January 28, 2025 at 09:07:28 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 8 y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }+66 y^{\prime \prime \prime }-41 y^{\prime \prime }-37 y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=-14\\ y^{\prime \prime }\left (0\right )&=-14\\ y^{\prime \prime \prime }\left (0\right )&=139\\ y^{\prime \prime \prime \prime }\left (0\right )&=-{\frac {29}{4}} \end{align*}

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 23

dsolve([8*diff(y(t),t$5)+4*diff(y(t),t$4)+66*diff(y(t),t$3)-41*diff(y(t),t$2)-37*diff(y(t),t)=0,y(0) = 4, D(y)(0) = -14, (D@@2)(y)(0) = -14, (D@@3)(y)(0) = 139, (D@@4)(y)(0) = -29/4],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.241 (sec). Leaf size: 79

DSolve[{8*D[ y[t],{t,5}]+4*D[y[t],{t,4}]+66*D[ y[t],{t,3}]-41*D[y[t],{t,2}]-37*D[y[t],t]==0,{y[0]==4,Derivative[1][y][0] ==-14,Derivative[2][y][0] ==-14,Derivative[3][y][0]==139,Derivative[4][y][0]==-29/4}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \int _1^t-\frac {1}{2} e^{-\frac {K[1]}{2}} (27 \cos (3 K[1])+14 \sin (3 K[1])+1)dK[1]-\int _1^0-\frac {1}{2} e^{-\frac {K[1]}{2}} (27 \cos (3 K[1])+14 \sin (3 K[1])+1)dK[1]+4 \]