74.13.28 problem 45

Internal problem ID [16394]
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 : 45
Date solved : Tuesday, January 28, 2025 at 09:07:27 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=3\\ y^{\prime \prime }\left (0\right )&=-7\\ y^{\prime \prime \prime }\left (0\right )&=15 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 15

dsolve([diff(y(t),t$4)-5*diff(y(t),t$2)+4*y(t)=0,y(0) = -1, D(y)(0) = 3, (D@@2)(y)(0) = -7, (D@@3)(y)(0) = 15],y(t), singsol=all)
 

\[ y = {\mathrm e}^{-t}-2 \,{\mathrm e}^{-2 t} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 16

DSolve[{D[y[t],{t,4}]-5*D[y[t],{t,2}]+4*y[t]==0,{y[0]==-1,Derivative[1][y][0] ==3,Derivative[2][y][0] ==-7,Derivative[3][y][0]==15}},y[t],t,IncludeSingularSolutions -> True]
 

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