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

Find out solutions to second order differential equations, Find out some so...

Find out some solutions to y′′ - 9 y = 0 Solution  We can find some solutions here simply through inspection. We require functions whose second derivative is 9 times the

If an item costs $1.45 to what amount will louise round, Louise is estimati...

Louise is estimating the cost of the groceries in her cart. She rounds the cost of every item to the nearest dollar to form her calculations. If an item costs $1.45, to what amount

Geometry, can i get some triangle congruence proofs help?

can i get some triangle congruence proofs help?

Example of imaginary numbers, Example of Imaginary Numbers: Example 1...

Example of Imaginary Numbers: Example 1: Multiply √-2  and √-32 Solution: (√-2)( √-32) = (√2i)( √32i) =√64 (-1) =8 (-1) =-8 Example 2: Divid

VECTOR, the sum of the vector QR, -SR, TQ and 2ST is?

the sum of the vector QR, -SR, TQ and 2ST is?

Shares and dividend, A man invests rs.10400 in 6%shares at rs.104 and rs.11...

A man invests rs.10400 in 6%shares at rs.104 and rs.11440 in 10.4% shares at rs.143.How much income would he get in all??

The distributive law, The Distributive Law :  If you were asked to mentall...

The Distributive Law :  If you were asked to mentally multiply 37 with 9, how would you proceed? 1 would do it as follows - 37 is 30 + 7, 30 x 9 = 270, 7 x 9 = 63, so 270 + 63, th

Matrices, Give me the assignment on the matrices...

Give me the assignment on the matrices...

Division of complex number, Division of complex number Now, we gave thi...

Division of complex number Now, we gave this formula a long with the comment that it will be convenient while it came to dividing complex numbers so let's look at a couple of e

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