Solution to an initial value problem, Mathematics

Assignment Help:

Solve the subsequent IVP.

dv/dt = 9.8 - 0.196v;               v(0) = 48

Solution

To determine the solution to an Initial Value Problem we should first determine the general solution to the differential equation and after that use the initial condition to recognize the precise solution which we are after. Thus, since this is the similar differential equation as we looked at in Illustration 1, we previously have its general solution.

v(t) = 50 + ce-0.196t

Currently, to determine the solution we are after we require identifying the value of c which will give us the solution we are after. To do such we simply plug in the first condition that will provide us an equation we can resolve for c. Thus let's do this as:

48 = v () = 50 + c ⇒ c = -2

Therefore, the actual solution to the Initial Value Problem is.

v(t) = 50  - 2 e-0.196t

A graph of this solution can be observed in the figure above.

Let's do a couple of illustrations which are a little more included.


Related Discussions:- Solution to an initial value problem

Find the coordinates of c , Plot the points A(2,0) and B (6,0) on a graph p...

Plot the points A(2,0) and B (6,0) on a graph paper. Complete an equilateral triangle ABC such that the ordinate of C be a positive real number .Find the coordinates of C   (Ans: (

Multiply, 37x7= multiply answer it.

37x7= multiply answer it.

How long will the board be after he makes the cut, Tom is cutting a piece o...

Tom is cutting a piece of wood to form a shelf. He cut the wood to 3.5 feet, but it is too long to fit in the bookshelf he is forming. He decides to cut 0.25 feet off the board. Ho

Derivatives of exponential and logarithm functions, Derivatives of Exponent...

Derivatives of Exponential and Logarithm Functions : The next set of functions which we desire to take a look at are exponential & logarithm functions. The most common exponentia

Basic, 8l550ml - 1/4l =

8l550ml - 1/4l =

Measures of skewness-measure of central tendency, Measures Of Skewness ...

Measures Of Skewness - These are numerical values such assist in evaluating the degree of deviation of a frequency distribution from the general distribution. - Given are t

Differentiate inside function in chain rule, Differentiate following. f ...

Differentiate following. f ( x ) = sin (3x 2   + x ) Solution It looks as the outside function is the sine & the inside function is 3x 2 +x. The derivative is then.

All subjects, I need help. Is there anyone there to help me?

I need help. Is there anyone there to help me?

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