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

Arden''s Theorem, Find the Regular Grammar for the following Regular Expres...

Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.

Geometry of convex sets, (a) Given a norm jj jj on Rn, express the closed b...

(a) Given a norm jj jj on Rn, express the closed ball in Rn of radius r with center c as a set. (b) Given a set A and a vector v, all contained in Rn, express the translate of A by

Integration and differentiation, Integration and Differentiation Diffe...

Integration and Differentiation Differentiation deals along with the determination of the rates of change of business activities or merely the process of finding the derivativ

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

Differential equation, Question: In the interest of saving up enough mo...

Question: In the interest of saving up enough money for retirement, you have created a bank account to store a  sum of money. Compound interest on  this account is accumulated

Combination, Combination A combination is a group of times whether ord...

Combination A combination is a group of times whether order is not significant. For a combination to hold at any described time it must comprise of the same items however i

Show that the vector is in the perfect matching polytope, 1.  Let G = (V,E)...

1.  Let G = (V,E) be a graph for which all nodes have degree 5 and where G is 5-edge is connected. a) Show that the vector x which is indexed by the edges E and for which x e =

Time & distance., Q4. Assume that the distance that a car runs on one liter...

Q4. Assume that the distance that a car runs on one liter of petrol varies inversely as the square of the speed at which it is driven. It gives a run of 25km per liter at a speed o

Find lim sup, 1.find lim sup Ek and liminf Ek of Ek=[(-(1/k),1] for k odd a...

1.find lim sup Ek and liminf Ek of Ek=[(-(1/k),1] for k odd and liminf Ek=[(-1,(1/k)] for k even.  2.Show that the set E = {x in R^2 : x1, x2 in Q} is dense in R^2.  3.let r>0 an

Derivatives of trig functions, Derivatives of Trig Functions In this s...

Derivatives of Trig Functions In this section we will see derivatives of functions other than polynomials or roots of polynomials. We'll begin this process off through taking

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