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

Problem, if .77x + x = 8966.60, what is the value of x?

if .77x + x = 8966.60, what is the value of x?

Find common denominators, Q. Find Common Denominators? What does it mea...

Q. Find Common Denominators? What does it mean? Say you have two fractions, like 1/3 and 8/21 And they have different denominators (3 and 21). Sometimes, you'd prefer

Comparison-types of word problems related to subtraction, Comparison - the...

Comparison - the difference between two groups or numbers, namely, how much one is greater than the other, how much more is in one group than in the other. (e.g., if Munna has

Factorization example, Example  Factorize x 2 - 4x + 4. If ...

Example  Factorize x 2 - 4x + 4. If we substitute x = 1, the value of the expression will be (1) 2 - 4(1) + 4 = 1 If we substitute x = -1, the value o

The prerequisites for multiplication, THE PREREQUISITES FOR MULTIPLICATION ...

THE PREREQUISITES FOR MULTIPLICATION : The word 'multiply', used in ordinary language, bears the meaning 'increase enormously For instance, bacteria multiply in favourable conditi

Determine the determinant of matrix, Example Determinant:   Determine ...

Example Determinant:   Determine the determinant of each of the following matrices. Solution : For the 2 x 2 there isn't much to perform other than to plug this in

Precalculus, Find the standard form of the equation of the parabola with a ...

Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, -7).

Determine the taylor series, Example : Determine the Taylor series for f(x)...

Example : Determine the Taylor series for f(x) = e x about x=0. Solution It is probably one of the easiest functions to get the Taylor series for. We just require recallin

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