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

Problem, if .77x + x = 8966.60, what is the value of x?

if .77x + x = 8966.60, what is the value of x?

Demerits and merit-the mode, The mode Merits i.  This can be dete...

The mode Merits i.  This can be determined from incomplete data given the observations along with the highest frequency are already known ii.  The mode has some applic

How much wrapping paper will needed, Barbara is packing a wedding gift that...

Barbara is packing a wedding gift that is contained within a rectangular box 20 by 18 by 4 in. How much wrapping paper will she require? a. 512 in 2 b. 1,440 in 2 c. 1,0

Binimial, theory behind the greatest term in the binomial expansion

theory behind the greatest term in the binomial expansion

Negative and positives, in 1970 a record 1.5 of rain fell in one minute at ...

in 1970 a record 1.5 of rain fell in one minute at Basse Terre, guadaloupe in the caribbnean.at this rate, how much rain fell in 3 seconds or 0.05 of a minutes?

.fractions, what is the difference between North America''s part of the tot...

what is the difference between North America''s part of the total population and Africa''s part

How to calculate arithmetic average or mean, Q. How to calculate arithmetic...

Q. How to calculate arithmetic average or mean? Ans. When people collect information, or data, they can easily be overwhelmed with information. Just imagine listing the b

Working definition of function, A function is an equation for which any x w...

A function is an equation for which any x which can be plugged into the equation will yield accurately one y out of the equation. There it is. i.e. the definition of functions w

Integrals involving quadratics - integration techniques, Integrals Involvin...

Integrals Involving Quadratics To this point we have seen quite some integrals which involve quadratics.  Example of Integrals Involving Quadratics is as follow: ∫ (x / x 2

Upper limit of normal , Frequently, tests that yield abnormal results are r...

Frequently, tests that yield abnormal results are repeated for confirmation.  What is the probability that for a usual person a test will be at least 1.5 times as high as the upper

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