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

Trigonometric ratios, to difine trigonometric ratios of an angle,is it nece...

to difine trigonometric ratios of an angle,is it necessary that the initial ray of the angle must be positive x-axis?

Shortcuts of fraction and squareroot, I am student of M.com and also doing...

I am student of M.com and also doing practice to crack bank or other competitive exam..please tell me shortcuts

Matrix of r, Let R be the relation on S = {1, 2, 3, 4, 5} defined by R =...

Let R be the relation on S = {1, 2, 3, 4, 5} defined by R = {(1,3); (1, 1); (3, 1); (1, 2); (3, 3); (4, 4)}. (b) Write down the matrix of R. (c) Draw the digraph of R.

Using substitution solving polynomial equations, Using Substitution Solving...

Using Substitution Solving Polynomial Equations ? Solve : (x 3 + 4) 2 - 15 (x 3 + 4) + 36 = 0. You might be tempted to multiply everything out and factor. However, there

Explain peano''s axioms with suitable example, Question 1 Explain Peano's ...

Question 1 Explain Peano's Axioms with suitable example Question 2 Let A = B = C= R, and let f: A→ B, g: B→ C be defined by f(a) = a+1 and g(b) = b 2 +1. Find a) (f °g

Give an example of divisibility, Give an example of Divisibility? If yo...

Give an example of Divisibility? If you can divide one number by another without getting a remainder, we say that the first number is divisible by the second. For instance, the

Coefficient of determination, Coefficient of Determination It refers t...

Coefficient of Determination It refers to the ratio of the explained variation to the total variation and is utilized to measure the strength of the linear relationship. The s

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