The method of successive approximations (see Section 2.8) can also be applied to systemsof equations. For example, consider the initial value problemx' = Ax,x (0) = x°,where A is a constant matrix and æ° is a prescribed vector.(a) Assuming that a solution x = 6(t) exists, show that it must satisfy the integralequation$(t) =2° +Αφ(s) ds.(4)

Given that x'=Ax with the initial condition x0=x0, where A is a constant matrix and x0 is a…

The method of successive approximations (see Section 2.8) can also be applied to systems of equations. For example, consider the initial value problem x' = Ax, æ(0) = x°, where A is a constant matrix and a° is a prescribed vector. (a) Assuming that a solution a = equation $(t) exists, show that it must satisfy the integral $(t) = x° + A6(s) ds. (4)

The method of successive approximations (see Section 2.8) can also be applied to systems of equations. For example, consider the initial value problem x' = Ax, æ(0) = x°, where A is a constant matrix and a° is a prescribed vector. (a) Assuming that a solution a = equation $(t) exists, show that it must satisfy the integral $(t) = x° + A6(s) ds. (4)

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

The method of successive approximations (see Section 2.8) can also be applied to systems
of equations. For example, consider the initial value problem
x' = Ax,
x (0) = x°,
where A is a constant matrix and æ° is a prescribed vector.
(a) Assuming that a solution x = 6(t) exists, show that it must satisfy the integral
equation
$(t) =
2° +
Αφ(s) ds.
(4)

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