dy dy + 12y = 0, (y(t) is the position at time t) dt2 dt (i) Rewrite the given second order differential equation as a system of first order differential equations for an unknown vector function Y() = ( ). y(t) v(t) (v(t) is the velocity at time t) (ii) Find two nonzero solutions of the differential equation that are not multiples of one another by seeking them in the form y(t) = est (iii) Use (ii) to find both straight line vector solutions of the system in (i)

dy dy + 12y = 0, (y(t) is the position at time t) dt2 dt (i) Rewrite the given second order differential equation as a system of first order differential equations for an unknown vector function Y() = ( ). y(t) v(t) (v(t) is the velocity at time t) (ii) Find two nonzero solutions of the differential equation that are not multiples of one another by seeking them in the form y(t) = est (iii) Use (ii) to find both straight line vector solutions of the system in (i)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Suppose that the damped harmonic oscil-lator is governed by the second order linear differential equation

dy
dy
12y = 0, (y(t) is the position at time t)
dt
dt2
(i) Rewrite the given second order differential equation as a system of first
order differential equations for an unknown vector function
y(t)
v(t)
Y(t) =
(v(t) is the velocity at time t)
(ii) Find two nonzero solutions of the differential equation that are not
multiples of one another by seeking them in the form y(t) = est
(iii) Use (ii) to find both straight line vector solutions of the system in (i)

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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