dy = 3x – Y dt dx 4x + 2y, dt (i) Show that x(t) = 10e5t –- e-2t and y(t) = 5e5t + 3e2t form a solution (ii) Rewrite the solution in (i) in the form Y(t) = (8) = e^itv1 + e*stv2 x(t) y(t) please note that you do not need to compute eigenvalues and eigenvec- tors, just rewrite what is given in (i) (iii) Find Y(0)

dy = 3x – Y dt dx 4x + 2y, dt (i) Show that x(t) = 10e5t –- e-2t and y(t) = 5e5t + 3e2t form a solution (ii) Rewrite the solution in (i) in the form Y(t) = (8) = e^itv1 + e*stv2 x(t) y(t) please note that you do not need to compute eigenvalues and eigenvec- tors, just rewrite what is given in (i) (iii) Find Y(0)

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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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

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Consider the system of linear differential equations:

dy
= 3x – Y
dt
dx
4x + 2y,
dt
(i) Show that x(t) = 10e5t –- e-2t and y(t) = 5e5t + 3e2t form a solution
(ii) Rewrite the solution in (i) in the form Y(t) = (8) = e^itv1 + e*stv2
x(t)
y(t)
please note that you do not need to compute eigenvalues and eigenvec-
tors, just rewrite what is given in (i)
(iii) Find Y(0)

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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