Abels theorem, Mathematics

Assignment Help:

If y1(t) and y2(t) are two solutions to

y′′ + p (t ) y′ + q (t ) y = 0

So the Wronskian of the two solutions is,

1583_Abels Theorem.png W(y1,y2)(t) =

=                                    for some t0.

Since we don't know the Wronskian and we don't know t0 this won't do us many good apparently. Though, we can rewrite as

W(y1,y2)(t) = ce-p(t) dt  ...................................(3)

Here the original Wronskian sitting opposite the exponential is absorbed in the c and the evaluation of the integral at t0 will place a constant in the exponential such can also be brought out and absorbed in the constant c. Whether you don't recall how to do this return and take see the linear, first order differential equation section that we did something the same there.

Along with this rewrite we can calculate the Wronskian up to a multiplicative constant, that isn't too bad. See as well that we don't in fact need the two solutions to do that.  All we require is the coefficient of the first derivative from the differential equation and provided the coefficient of the second derivative is one also.


Related Discussions:- Abels theorem

Sum of a number of terms in g.p., We know that the terms in G.P. are:...

We know that the terms in G.P. are: a, ar, ar 2 , ar 3 , ar 4 , ................, ar n-1 Let s be the sum of these terms, then s = a + ar + ar 2

Evaluate the diameter of the pizza box, If the area of a small size pizza i...

If the area of a small size pizza is 78.5 in 2 , what size pizza box would required for the small pizza? (Note: Pizza boxes are calculated according to the length of one side.)

Find the value of ((a+b)/(a-b)) , If arg (a/b) = pi/2, then find the value ...

If arg (a/b) = pi/2, then find the value of ((a+b)/(a-b)) where a,b are complex numbers. Ans) Arg (a/b) =Pi/2 Tan-1   (a/b)=   Pi/2 A/B = tanP/2 ,therefore a/b=infinity.

What is approximation, approximate value is the precise or the accurate val...

approximate value is the precise or the accurate value which is measured  to the actual value.., approximation is how close the measured value is to the actual value , for example

Statistics, Calculate the Kendaul''s correlation cofficient for a given dat...

Calculate the Kendaul''s correlation cofficient for a given data.

Solid, The lateral edge of a pyramidal church spire is 61feet.Each side of ...

The lateral edge of a pyramidal church spire is 61feet.Each side of its octagonal base is 22feet. What will be the cost of painting the spire at 2.5 cents a square foot

Chanllenge, a pizza driver delivered 27 pizzas in one night he delivered mo...

a pizza driver delivered 27 pizzas in one night he delivered more then one pizza to only one house . every other house he only delivered pizza to 18 houses . how many pizzas did he

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

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