86.6.4 problem 4

Internal problem ID [23137]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 5. Linear equations of the second order with constant coefficients. Exercise 5b at page 77
Problem number : 4
Date solved : Thursday, October 02, 2025 at 09:23:22 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 9 y^{\prime \prime }+49 y&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.016 (sec). Leaf size: 17

ode:=9*diff(diff(y(x),x),x)+49*y(x) = 0; 
ic:=[y(0) = 3, D(y)(0) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {3 \sin \left (\frac {7 x}{3}\right )}{7}+3 \cos \left (\frac {7 x}{3}\right ) \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 24

ode=9*D[y[x],{x,2}]+49*y[x]==0; 
ic={y[0]==3,Derivative[1][y][0] ==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {3}{7} \left (\sin \left (\frac {7 x}{3}\right )+7 \cos \left (\frac {7 x}{3}\right )\right ) \end{align*}

✓ Sympy. Time used: 0.040 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(49*y(x) + 9*Derivative(y(x), (x, 2)),0) 
ics = {y(0): 3, Subs(Derivative(y(x), x), x, 0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {3 \sin {\left (\frac {7 x}{3} \right )}}{7} + 3 \cos {\left (\frac {7 x}{3} \right )} \]