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

Bernoulli differential equations, In this case we are going to consider dif...

In this case we are going to consider differential equations in the form, y ′ +  p   ( x ) y =  q   ( x ) y n Here p(x) and q(x) are continuous functions in the

.., rectangles 7cm by 4cm

rectangles 7cm by 4cm

SIMPLE INTEREST, A payday loan company charges a $95 fee for a $500 payday ...

A payday loan company charges a $95 fee for a $500 payday loan that will be repaid in 11 days. Treating the fee as interest paid, what is the equivalent annual interest rate?

Geometry, geometry fbw = 128 saf= 104 what is rfd

geometry fbw = 128 saf= 104 what is rfd

Integrated marketing, #question.Explain its nature and how it influences th...

#question.Explain its nature and how it influences the integrated marketing communications mix and distinguish between tactical and strategic use of integrated marketing communicat

Find the area of the shaded region of square, In the adjoining figure, ABCD...

In the adjoining figure, ABCD is a square of side 6cm.  Find the area of the shaded region. Ans:    From P draw PQ ⊥ AB AQ = QB = 3cm (Ans: 34.428 sq cm) Join PB

Geometry, can i get some triangle congruence proofs help?

can i get some triangle congruence proofs help?

Explain the vertex formula, Explain the Vertex Formula ? The vertex for...

Explain the Vertex Formula ? The vertex formula is a convenient way of finding the vertex of the graph for any quadratic function. The graph of the quadratic equation f(x) = ax

Formular for x and y, I have a simple right angle triangle. All I am given...

I have a simple right angle triangle. All I am given is h (the hypotenuse) and that ratio of x:y is 2:3. What is the formula to find x and y in terms of h?

Two consecutive integers is 15 find out the larger integer, If the differen...

If the difference among the squares of two consecutive integers is 15 find out the larger integer. Let x = the lesser integer and let x + 1 = the greater integer. The sentence,

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