7.9.5 problem 17

Internal problem ID [253]
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 2.2 (General solutions of linear equations). Problems at page 122
Problem number : 17
Date solved : Wednesday, February 05, 2025 at 03:06:18 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+9 y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-1\\ y^{\prime \prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 18

dsolve([diff(y(x),x$3)+9*diff(y(x),x)=0,y(0) = 3, D(y)(0) = -1, (D@@2)(y)(0) = 2],y(x), singsol=all)
 

\[ y = \frac {29}{9}-\frac {\sin \left (3 x \right )}{3}-\frac {2 \cos \left (3 x \right )}{9} \]

✓ Solution by Mathematica

Time used: 0.110 (sec). Leaf size: 23

DSolve[{D[y[x],{x,3}]+9*D[y[x],x]==0,{y[0]==3,Derivative[1][y][0] ==-1,Derivative[2][y][0] ==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{9} (-3 \sin (3 x)-2 \cos (3 x)+29) \]