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

Inverse functions, Inverse Functions : In the last instance from the pr...

Inverse Functions : In the last instance from the previous section we looked at the two functions   f ( x ) = 3x - 2 and g ( x ) = x /3+ 2/3 and saw that ( f o g ) ( x )

Find the area of the rhombus, Show that the points (3, 0), (4, 5), (-1, 4) ...

Show that the points (3, 0), (4, 5), (-1, 4) and (-2, -1) taken in order are the vertices of a rhombus. Also find the area of the rhombus.

Show that of all right triangles inscribed in a circle, Show that of all ri...

Show that of all right triangles inscribed in a circle, the triangle with maximum perimeter is isosceles.

Find out least common multiple, Find out Least Common Multiple? The sma...

Find out Least Common Multiple? The smallest number that is a common multiple of two numbers (that is, both numbers share the same multiple) is called the least common multiple

Divide 6.8 × 105 by 2.0 × 102 write your answer scientific, Divide 6.8 × 10...

Divide 6.8 × 10 5 by 2.0 × 10 2 . Write your answer in scientific notation? To divide numbers written in scienti?c notation and divide the ?rst numbers (6.8 ÷ 2.0 = 3.4); the

Trig substitutions - integration techniques, Trig Substitutions - Integrati...

Trig Substitutions - Integration techniques As we have completed in the last couple of sections, now let's start off with a couple of integrals that we should previously be

Estimate the distance to this star, To find the distance to nearby stars, t...

To find the distance to nearby stars, the method of parallax is used. The idea is to find a triangle with the star at one vertex and with a base as large as possible. To do this, t

Calculate the limit of f (-4), Let's take a look at one more example to ens...

Let's take a look at one more example to ensure that we've got all the ideas about limits down that we've looked at in the last couple of sections. Example: Given the below gr

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