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

Quadratic equation, If roots of (x-p)(x-q) = c are a and b what will be th...

If roots of (x-p)(x-q) = c are a and b what will be the roots of (x-a)(x-b) = -c please explain. Solution)  (x-p)(x-q)=c x2-(p+q)x-c=0 hence,   a+b=p+q  and    a.b=pq-c

Parabola, please i need the answers to x^_7x+10 i want the vertex,axis of s...

please i need the answers to x^_7x+10 i want the vertex,axis of semetery,y intersect and the x intercept

Perform algebraic operation , Perform each of the following algebraic expr...

Perform each of the following algebraic expression as instruction says;- I.Multiply 5x+6m+4y by5 II.Divide 4ax+6ay-10az by 2a

Add subtract fractions., how do you add and subtract mixed numbers with fra...

how do you add and subtract mixed numbers with fractions

What is the ratio of the areas of sectors , What is the ratio of the areas ...

What is the ratio of the areas of sectors I and II ?                               (Ans:4:5) Ans:    Ratio will be 120/360  Π r 2 : 150/360  Π r 2 4/12  : 5/12  =

Montel''s Theorem, In 5 pages, please try to prove Theorem 3 based on Monte...

In 5 pages, please try to prove Theorem 3 based on Montel''s Theorem. please use "Latex" Knuth Donald to write this paper. It is known that Theorem 3 on page 137 of the attached

What is the square root of -i and argument of -i, What is the square root o...

What is the square root of -i and argument of -i Ans) argument of -i is 270 ad 1 is the square root of -i

Algebraic word problems, Algebraic Word Problems: Equations: 1....

Algebraic Word Problems: Equations: 1. The total electrical output of one nuclear facility is 200 megawatts more than that of another nuclear facility. Let L be the

Matrices, (e) Solve the following system of equations by using Matrix meth...

(e) Solve the following system of equations by using Matrix method. 3x + 2y + 2z = 11 x + 4y + 4z = 17 6x + 2y + 6z = 22

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