71.9.12 problem 14

Internal problem ID [14491]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.1, page 186
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 06:42:26 AM
CAS classification : [[_3rd_order, _missing_x]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 6

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

\[ y = \cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 60.010 (sec). Leaf size: 33

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

\[ y(x)\to \int _1^x-\sin (K[1])dK[1]-\int _1^0-\sin (K[1])dK[1]+1 \]