Find the solution to initial value problem, Mathematics

Assignment Help:

Illustration:  Find the solution to the subsequent IVP.

ty' + 2y = t2 - t + 1,      y(1) = ½

Solution:

Initially divide via the t to find the differential equation in the accurate form.

y' + (2/t) Y = t - 1 + 1/t

Currently let's find the integrating factor, µ(t):

753_Find the solution to initial value problem.png

Currently, we require to simplify µ(t). Although, we can't utilize (11) as which needs a coefficient of one in front of the logarithm.  Thus, recall as

In xr = r In x

And rewrite the integrating factor in a form which will permit us to simplify this.

µ(t) = e 2In|t| = eIn|t|2 = |t|2 = t2

We were capable to drop the absolute value bars here as we were squaring the t, but frequently they can't be dropped therefore be careful along with them and don't drop them unless you identify that you can. Frequently the absolute value bars must continue

Here, multiply the rewritten differential equation but remember that we can't utilize the original differential equation here, through the integrating factor.

(t2y)' = t3 - t2 + t

Integrate both sides and resolve for the solution.

t2y = ∫t3 - t2 + t dt

= ¼t4 - ? t3 + t dt

 y(t) = ¼t2 - ? t3+ ½ + c/t2

At last, apply the initial condition to find the value of c.

½ = y(1) = ¼ - 1/3 + ½ + c ⇒ c= 1/12

The solution is afterward,

y(t) = ¼t2 - ? t3+ ½ + 1/12t2

Now is a plot of the solution.

1061_Find the solution to initial value problem1.png


Related Discussions:- Find the solution to initial value problem

Modi method, why modi method is used in operation research

why modi method is used in operation research

Normal approximation to binomial to approximate probability, A certain flig...

A certain flight arrives on time 78% of the time. Suppose 1000 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that a)

Algebria, solve and graph the solution set 7x-4 > 5x + 0

solve and graph the solution set 7x-4 > 5x + 0

Sketch the graph of h (t ) = 1 - 5e 1/(t/2), Sketch the graph of h (t ) = ...

Sketch the graph of h (t ) = 1 - 5e  1/(t/2) Solution : Let's primary get a table of values for this function. Following is the sketch. The major point behin

Compare and contrast african immigrants, Compare and contrast African immig...

Compare and contrast African immigrants with our immigrant groups? How are they different? What are the implications of these differences for their adjustment to the larger society

Curve tracing, How we calculate region for curve tracing

How we calculate region for curve tracing

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

SHOPPERS`STOP, 3. How are Indian customers visiting Shoppers’ Stop any diff...

3. How are Indian customers visiting Shoppers’ Stop any different from customers of developed western countries? 4. How should Shoppers’ Stop develop its demand forecasts?

Sqrt n- sqrt 8836, How many integers satisfy (sqrt n- sqrt 8836)^2 Solutio...

How many integers satisfy (sqrt n- sqrt 8836)^2 Solution) sqrt 8836 = 94 , let sqrt n=x the equation becomes... (x-94)^2 (x-94)^2 - 1 (x-95)(x-93) hence  93 8649  the number o

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