Find out solutions to second order differential equations, Mathematics

Assignment Help:

Find out some solutions to

y′′ - 9 y = 0

Solution

 We can find some solutions here simply through inspection. We require functions whose second derivative is 9 times the original function. One of the first functions which I can think of that comes back to it after two derivatives is an exponential function and along with proper exponents the 9 will find taken care of as well.

Therefore, it looks like the subsequent two functions are solutions.

y(t) = e3t and    y(t) = e-3t

We'll leave this to you to verify that these are actually solutions.

These two functions are not the merely solutions to the differential equation though. Any of the subsequent is also solutions to the differential equation.

y (t ) = -9e3t

y (t ) = 56e-3t

y (t ) = 7e3t  - 6e-3t

 y (t ) = 123e3t

y (t ) = (14/9) e-3t

y (t )= -92e3t  -16e-3t

 Actually, if you think about it any function which is in the form

y (t ) = c e3t  + c e-3t will be a solution to the differential equation.

This illustration leads us to a very significant fact that we will use in practically each problem in this section will be a solution to the differential equation.


Related Discussions:- Find out solutions to second order differential equations

Prove that ar= 3/7 ac of parallelogram , ABCD is a parallelogram in the giv...

ABCD is a parallelogram in the given figure, AB is divided at P and CD and Q so that AP:PB=3:2 and CQ:QD=4:1. If PQ meets AC at R, prove that AR= 3/7 AC. Ans:    ΔAPR ∼ Δ

System of linear equations, create a system of linear equations that has (2...

create a system of linear equations that has (2,3)as a solution.

Determine the length of the longer base, The longer base of a trapezoid is ...

The longer base of a trapezoid is 3 times the shorter base. The nonparallel sides are congruent. The nonparallel side is 5 cm more that the shorter base. The perimeter of the trape

Trig functions:, Trig Functions: The intent of this section is introducing...

Trig Functions: The intent of this section is introducing you of some of the more important (from a Calculus view point...) topics from a trig class.  One of the most significant

Estimating sums, round to the nearest ten to estimate , 422+296

round to the nearest ten to estimate , 422+296

Travel time, you are driving on a freeway to a tour that is 500 kilometers ...

you are driving on a freeway to a tour that is 500 kilometers from your home. after 30 minutes , you pass a freeway exit that you know is 50 kilometer from your home. assuming that

Shares and dividend, how should i make my project on these topic?

how should i make my project on these topic?

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