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

Logarithms, How to solve this: log x(81) = 4

How to solve this: log x(81) = 4

College Algebra, I am looking for a tutor in College Algebra

I am looking for a tutor in College Algebra

Find Equation of the circle, The line 4x-3y=-12 is tangent at the point (-3...

The line 4x-3y=-12 is tangent at the point (-3,0) and the line 3x+4y=16 is tangent at the point (4,1). find the equation of the circle. solution) well you could first find the ra

Simple equations, three times the first of the three consecutive odd intege...

three times the first of the three consecutive odd integers is 3 more than twice the third integer. find the third integer.

Find the area of shaded region, Find the area of shaded region, if the side...

Find the area of shaded region, if the side of square is 28cm and radius of the sector is ½ the length of side of square.

Rhjuu, Ask questutfjion #Minimum 100 words accepted#

Ask questutfjion #Minimum 100 words accepted#

Distribution of sample means not normal, The distribution of sample means i...

The distribution of sample means is not always a normal distribution. Under what circumstances is the distribution of sample means not normal?

We know this equation a°=1.prove this?, we know that    A^m/A^m=1         ...

we know that    A^m/A^m=1                    so A^(m-m)=1                    so A^0=1.....

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