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

Transpose of a matrix, I didn't understand the concept of Transpose of a Ma...

I didn't understand the concept of Transpose of a Matrix, need assistance.

Shares and dividend, how should i make my project on these topic?

how should i make my project on these topic?

Example of identify the pre-requisites, Ravi is a teacher of Class 4 in a m...

Ravi is a teacher of Class 4 in a municipal school in Delhi. When the new school year started, he opened the textbook and started teaching the children how to write 4-digit numbers

Taylor series - sequences and series, Taylor Series - Sequences and Series ...

Taylor Series - Sequences and Series In the preceding section we started looking at writing down a power series presentation of a function.  The difficulty with the approach

Find the normal to any point on the surface of convex lenses, Draw a tangen...

Draw a tangent on the lens where you want to find normal .Then line perpendicular to tangent gives normal at that point.

Bussiness, How do these websites help the company strengthen its relationsh...

How do these websites help the company strengthen its relationships with its stakeholders? List the website(s) that you previewed and give examples to support your answers. Who are

Rolles therom, f(x)=sin x+cos x in the interval {0,90}

f(x)=sin x+cos x in the interval {0,90}

Example of rounding off, Example of Rounding Off: Example: Round ...

Example of Rounding Off: Example: Round off the subsequent number to two decimal places. 6.238 Solution: Step 1:             8 is the number to the right of t

SIMPLE INTEREST, A payday loan company charges a $95 fee for a $500 payday ...

A payday loan company charges a $95 fee for a $500 payday loan that will be repaid in 11 days. Treating the fee as interest paid, what is the equivalent annual interest rate?

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