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

Mrs, Distributive Property _x7=(3x7)+(2x_)

Distributive Property _x7=(3x7)+(2x_)

Trigonometry, how to change sin 24 degree in digits?

how to change sin 24 degree in digits?

5th grade, 6 and 3/8 minus 1 and 3/4

6 and 3/8 minus 1 and 3/4

NCCER, what is 9/16 Divided by 7/8

what is 9/16 Divided by 7/8

How high is a structure, One method of calculating the height of an object ...

One method of calculating the height of an object is to place a mirror on the ground and then position yourself so that the top of the object will be seen in the mirror. How high i

Solving trig equations, Solving Trig Equations : Here we will discuss on s...

Solving Trig Equations : Here we will discuss on solving trig equations. It is something which you will be asked to do on a fairly regular basis in my class. Let's just see the

Dy/dx, how do you differentiate sinx/ex?

how do you differentiate sinx/ex?

Rolles theorem, Rolle's Theorem  Assume f(x) is a function which satis...

Rolle's Theorem  Assume f(x) is a function which satisfies all of the following. 1. f(x) is continuous in the closed interval [a,b]. 2. f(x) is differentiable in the ope

Cartesian product of sets, The Cartesian product (also called as the cross ...

The Cartesian product (also called as the cross product) of two sets A and B, shown by AΧB (in the similar order) is the set of all ordered pairs (x, y) such that x€A and y€B. What

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