Reduction of order - fundamental set of solutions, Mathematics

Assignment Help:

Given that

2t2 y′′ + ty′ - 3 y = 0

Show that this given solution are form a fundamental set of solutions for the differential equation?

Solution

The two solutions from that illustration are

y1(t) = t-1          y2(t) = t3/2

Let's calculate the Wronskian of these two solutions.

1711_Reduction of Order - fundamental set of solutions.png

Therefore, the Wronskian will never be zero. Memorizes that we can't plug t = 0 in the Wronskian. It would be a problem in determining the constants in the general solution, except that we as well can't plug t = 0 in the solution either and thus this isn't the problem which it might appear to be.

So, as the Wronskian isn't zero for any t the two solutions form a fundamental set of solutions and the general solution is as

y(t) = c1t-1+ c2 t3/2as we claimed in that illustration.

To this point we're determined a set of solutions then we've claimed which they are actually a fundamental set of solutions. Certainly, you can now verify all those claims which we've made, though this does bring up a question.


Related Discussions:- Reduction of order - fundamental set of solutions

Calculate the average return, A department store faces a decision for a sea...

A department store faces a decision for a seasonal product for which demand can be high, medium or low. The purchaser can order 1, 2 or 3 lots of this product before the season beg

The sum of two consecutive integers is 41 integer, The sum of two consecuti...

The sum of two consecutive integers is 41. What are the integers? Two consecutive integers are numbers in sequence like 4 and 5 or -30 and -29, that are each 1 number apart. Le

Statistics, The winning team''s score in 21 high school basketball games wa...

The winning team''s score in 21 high school basketball games was recorded. If the sample mean is 54.3 points and the sample standard deviation is 11.0 points, find the 90% confiden

Evaluate the infinite limits of given limits, Evaluate following limits. ...

Evaluate following limits. Solution Therefore we will taking a look at a couple of one-sided limits in addition to the normal limit here. In all three cases notice

Differentiate outline function in chain rules, Differentiate following. ...

Differentiate following. Solution : It requires the product rule & each derivative in the product rule will need a chain rule application as well. T ′ ( x ) =1/1+(2x) 2

Cone - three dimensional spaces, Cone - Three dimensional spaces The be...

Cone - Three dimensional spaces The below equation is the general equation of a cone. X 2 / a 2 + y 2 /b 2 = z 2 /c 2 Here is a diagram of a typical cone. Not

#i need help on my math homework its on algabraitle.., The question is: If ...

The question is: If 0.2 x n = 1.4,what is the value of n.

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