7.11.39 problem 40

Internal problem ID [360]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 40
Date solved : Wednesday, February 05, 2025 at 03:24:38 AM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 20

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

\[ y = -5+\frac {5 \cos \left (x \right )}{2}+\frac {5 \,{\mathrm e}^{x}}{4}+\frac {5 \,{\mathrm e}^{-x}}{4} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 23

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

\[ y(x)\to \frac {5}{4} \left (e^{-x}+e^x+2 \cos (x)-4\right ) \]