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

Determine the quotient and remainder , Let a = 5200 and b = 1320. (a) If...

Let a = 5200 and b = 1320. (a) If a is the dividend and b is the divisor, determine the quotient q and remainder r. (b) Use the Euclidean Algorithm to find gcd(a; b). (c)

Initial recognition of the financial instruments, Grimm plc (Grimm) has the...

Grimm plc (Grimm) has the following transactions: a) On 1 st January 2010, Grimm issued 400,000 convertible £1 6% debentures for £600,000.  The professional fees associated wit

Algebra, sir i want to ask u a question and that is if we simplify this wha...

sir i want to ask u a question and that is if we simplify this what will be the answer.(9x-45z+6y-100z+5x)

Solid Mensuration, The two sides of a triangle are 17 cm and 28 cm long, an...

The two sides of a triangle are 17 cm and 28 cm long, and the length of the median drawn to the third side is equal to 19.5 cm. Find the distance from an endpoint of this median to

TRIGONOMETRY, EXPLAIN ME ABOUT ITS FUNCTIONS.

EXPLAIN ME ABOUT ITS FUNCTIONS.

Permutations and combinations, number of ways that a mixed doubles tennis g...

number of ways that a mixed doubles tennis game can be arranged from 7 couples if no husband and wife play in the same game is??

Trigonometry, if theta is a positive acute angle and 2sin theta +15cos squ...

if theta is a positive acute angle and 2sin theta +15cos square theta=7 then find the value of cot theta

Assignment, how do mathematical ideas grow?

how do mathematical ideas grow?

Fractions, if you have 1/5 of a candy bar and 4 friends how much will they ...

if you have 1/5 of a candy bar and 4 friends how much will they get

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