14.21.7 problem 7

Internal problem ID [2716]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.15, Higher order equations. Excercises page 263
Problem number : 7
Date solved : Monday, January 27, 2025 at 06:12:14 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}-2 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ 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 )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.022 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

Time used: 0.119 (sec). Leaf size: 25

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

\[ y(t)\to -\frac {t^2}{2}-2 t-e^t (t-3)-3 \]