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 order of the local truncation error, The backwards Euler diff...

The backwards Euler difference operator is given by for differential equation y′ = f(t, y). Determine the order of the local truncation error. Explain why this difference o

Algebra, solve x+y= 7 and x-y =21

solve x+y= 7 and x-y =21

Whta is truth table, What is a truth table? Distinguish between Tautology &...

What is a truth table? Distinguish between Tautology & Contradiction?

Geometry, What is the better buy?a square pizza measuring 8 inches by 8inch...

What is the better buy?a square pizza measuring 8 inches by 8inches that cost $10 or a round pizza with a 9 inch diameter that also cost $10?

Positive exponents, Simplify following and write the answers with only posi...

Simplify following and write the answers with only positive exponents.   (-10 z 2 y -4 ) 2 ( z 3 y ) -5 Solution    (-10 z 2 y -4 ) 2 ( z 3 y ) -5

Sum, As1212uestion #Minimum 100 words accepted#

As1212uestion #Minimum 100 words accepted#

Describe adding and subtracting square roots, Describe Adding and Subtracti...

Describe Adding and Subtracting Square Roots? To add or subtract square roots, the radicands must be the same. If the radicands are the same, add/subtract the coefficients (the

Linear Equations, y= -3x tell if it is linear or not. our teacher wants it ...

y= -3x tell if it is linear or not. our teacher wants it graphed or something.

Triangulos rectangulos y no rectangulos, el extremo de un poste que partió ...

el extremo de un poste que partió 8.45 metros de la base del poste y forma con el suelo un angulo de 40 grados 28 minutos.hallar la altura original del poste

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