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

Fraction word problem, castor brought 6 3/4 carat cakes to share with 26 st...

castor brought 6 3/4 carat cakes to share with 26 students. did castor bring enough for each student to have 1/4 of cake?

Mode, how to work out mode

how to work out mode

Ratios, a doctor sees 3 boys to 5 girls in one week . If he sees 40 boys in...

a doctor sees 3 boys to 5 girls in one week . If he sees 40 boys in one day then how many girls does he see that day

.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

How to converting decimals to percents, How to Converting Decimals to Perce...

How to Converting Decimals to Percents ? To convert a decimal to a percent: Move the decimal point two decimal places to the right. Place a percent sign after the resulting

Permutations and Combinations, How many 4 digit number lass than 6000 can b...

How many 4 digit number lass than 6000 can be made with the digits 7,6,4 and 2 if digits are not repeated?

Methods of sampling, a.      Random or probability sampling methods they in...

a.      Random or probability sampling methods they involve: Simple random sampling Systematic sampling Stratified sampling Multi stage sampling   b.

Multiplication in decimal notations., Consider the following multiplication...

Consider the following multiplication in decimal notations: (999).(abc)=def132 ,determine the digits a,b,c,d,e,f. solution) a=8 b=6 c=8 d=8 e=6 f=7 In other words, 999 * 877 = 8

Approximating solutions to equations newtons method, Approximating solution...

Approximating solutions to equations : In this section we will look at a method for approximating solutions to equations. We all know that equations have to be solved on occasion

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