74.13.33 problem 50

Internal problem ID [16399]
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 : 50
Date solved : Tuesday, January 28, 2025 at 09:07:29 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=16\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime \prime }\left (0\right )&=0\\ y^{\left (5\right )}\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 29

dsolve([diff(y(t),t$6)-3*diff(y(t),t$4)+3*diff(y(t),t$2)-y(t)=0,y(0) = 16, D(y)(0) = 0, (D@@2)(y)(0) = 0, (D@@3)(y)(0) = 0, (D@@4)(y)(0) = 0, (D@@5)(y)(0) = 0],y(t), singsol=all)
 

\[ y = \left (t^{2}+5 t +8\right ) {\mathrm e}^{-t}+{\mathrm e}^{t} \left (t^{2}-5 t +8\right ) \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 33

DSolve[{D[ y[t],{t,6}]-3*D[y[t],{t,4}]+3*D[y[t],{t,2}]-y[t]==0,{y[0]==16,Derivative[1][y][0] ==0,Derivative[2][y][0] ==0,Derivative[3][y][0]==0,Derivative[4][y][0]==0,Derivative[5][y][0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-t} \left (t^2+e^{2 t} \left (t^2-5 t+8\right )+5 t+8\right ) \]