Complex root - fundamental set of solutions, Mathematics

Assignment Help:

Example: Back into the complex root section we complete the claim that

y1 (t ) = elt cos(µt)        and      y2(t) = elt sin(µt)

Those were a basic set of solutions.  Prove that they actually are.

Solution

Thus, to prove this we will require to take find the Wronskian for these two solutions and show that this isn't zero.

1105_Complex root - fundamental set of solutions.png

= elt cos(µt)( lelt sin(µt) + µ elt cos(µt)) - elt sin(µt)( lelt cos(µt) - µ elt sin(µt))

= µ e2lt cos2(µt) + µ e2lt sin2(µt)

= µ e2lt( cos2(µt) + sin2(µt))

= µ e2lt

Here, the exponential will never be zero and µ ≠ 0 whether it were we wouldn't have complex roots and so W ≠ 0. Thus, these two solutions are actually a fundamental set of solutions and hence the general solution in this case is. As:

 y (t ) = c1elt cos (mt ) + c2eltsin (mt)


Related Discussions:- Complex root - fundamental set of solutions

probability , An engineer has 200 resistors that he keeps in one box. Resi...

An engineer has 200 resistors that he keeps in one box. Resistors are colored to help their identification, and in this box there are 30 white resistors, 50 black resistors, 80 red

Subtract, Ask question Minimum 100 words accepted# 1000-101

Ask question Minimum 100 words accepted# 1000-101

Sample space, Sample Space is the totality of all possible out...

Sample Space is the totality of all possible outcomes of an experiment. Hence if the experiment was inspecting a light bulb, the only possible outcomes

How will you use the Gantt chart for solving the sequencing, How will you u...

How will you use the Gantt chart for solving the sequencing problem?

Explain id amortisation is proper impairment will not arise, If depreciatio...

If depreciation/amortisation is done properly, impairment adjustments will not arise.   Required: Do you agree with the above statement? Critically and fully explain your

Find the external surface area, A shuttlecock used for playing badminton ha...

A shuttlecock used for playing badminton has the shape of a frustum of a Cone mounted on a hemisphere.  The external diameters of the frustum are 5 cm and 2 cm, and the height of t

Test of homogeneity , Test of homogeneity This is concerned along with...

Test of homogeneity This is concerned along with the proposition that several populations are homogenous along with respect to some characteristic of interest for example; one

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd