1.9.5 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 : Tuesday, September 30, 2025 at 03:54:15 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*}

✓ Maple. Time used: 0.053 (sec). Leaf size: 18

ode:=diff(diff(diff(y(x),x),x),x)+9*diff(y(x),x) = 0; 
ic:=[y(0) = 3, D(y)(0) = -1, (D@@2)(y)(0) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.065 (sec). Leaf size: 23

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

\begin{align*} y(x)&\to \frac {1}{9} (-3 \sin (3 x)-2 \cos (3 x)+29) \end{align*}

✓ Sympy. Time used: 0.096 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*Derivative(y(x), x) + Derivative(y(x), (x, 3)),0) 
ics = {y(0): 3, Subs(Derivative(y(x), x), x, 0): -1, Subs(Derivative(y(x), (x, 2)), x, 0): 2} 
dsolve(ode,func=y(x),ics=ics)
 

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