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

Decimals, how will the decimal point move when 245.398 is multiplied by 10

how will the decimal point move when 245.398 is multiplied by 10

Fractions, what is 1/3 + 2/9 equal

what is 1/3 + 2/9 equal

Multiple integrals, how to convert multiple integral into polar form and ch...

how to convert multiple integral into polar form and change the limits of itegration

Polynomials, write the zeros of underroot3power2 -8x+4underroot 3

write the zeros of underroot3power2 -8x+4underroot 3

Theory of sets, finite or infinite 1]A={4,5,6,....}

finite or infinite 1]A={4,5,6,....}

Proof integral function, Proof of: if f(x) > g(x) for a x b th...

Proof of: if f(x) > g(x) for a x b then a ∫ b  f(x) dx > g(x). Because we get f(x) ≥ g(x) then we knows that f(x) - g(x) ≥ 0 on a ≤ x ≤ b and therefore by Prop

Linear relations, determine the equation that represent the following lines...

determine the equation that represent the following lines be sure to define your variable and show all of your work

.fractions, what is the difference between North America''s part of the tot...

what is the difference between North America''s part of the total population and Africa''s part

Marginal cost & cost function, Marginal cost & cost function  The cost ...

Marginal cost & cost function  The cost to produce an additional item is called the marginal cost and as we've illustrated in the above example the marginal cost is approxima

Problem, a mixture of 40 liters of milk and water contains 10% water.how mu...

a mixture of 40 liters of milk and water contains 10% water.how much water should be added to this so that water my be 20% in the new mixture

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