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

Example of the commutative property of addition, Tori was asked to provide ...

Tori was asked to provide an example of the commutative property of addition. Which of the subsequent choices would be correct? Using the simple interest formula Interest = pr

Multiplication of two complex numbers, Multiply the given below and write t...

Multiply the given below and write the answer in standard form. (2 - √-100 )(1 + √-36 ) Solution If we have to multiply this out in its present form we would get,  (2 -

Equations, 20 equations that equal 36

20 equations that equal 36

Tied rankings, Tied Rankings A slight adjustment to the formula is mad...

Tied Rankings A slight adjustment to the formula is made if several students tie and have the similar ranking the adjustment is: (t 3 - t)/12 Whereas t = number of tied

Explain the counting principle in maths, Explain the Counting Principle in ...

Explain the Counting Principle in maths? The fundamental counting principle is used when you want to calculate the total number of possible outcomes (or combinations) of an exp

Mount everest is 29, Mount Everest is 29,028 ft high. Mount Kilimanjaro is ...

Mount Everest is 29,028 ft high. Mount Kilimanjaro is 19,340 ft high. How much taller is Mount Everest? Subtract Mt. Kilimanjaro's height from Mt. Everest's height; 29,028 - 19

Evaluate integrals (1 - (1 /w) cos (w - ln w) dw, Evaluate following integr...

Evaluate following integrals.                       ( (1 - (1 /w) cos (w - ln w) dw Solution In this case we know how to integrate only a cosine therefore let's makes th

Damping force, The subsequent force that we want to consider is damping. Th...

The subsequent force that we want to consider is damping. This force may or may not be there for any specified problem. Dampers work to counteract any movement. There are some w

Diffrential integral , All the integrals below are understood in the sense ...

All the integrals below are understood in the sense of the Lebesgue. (1) Prove the following equality which we used in class without proof. As-sume that f integrable over [3; 3]

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