Determine the solution to initial value problem, Mathematics

Find the solution to the subsequent IVP.

ty' - 2y = t5 sin(2t) - t3 + 4t4, y (π) = 3/2 π4

Solution: First, divide by t to find the differential equation in the accurate form.

y' - 2y/t = t4 sin(2t) - t2 + 4t3, y (π) = 3/2 π4

Here remember that we have done this we can get the integrating factor, µ(t).

µ(t)  = e∫(- 2y/t)dt  = e-2In|t|

Always remember that the "-" is part of p(t).  Forgetting such minus sign can take a difficulty that is extremely easy to do and turn it in an extremely difficult, if possible trouble so be careful!

Here, we just require simplifying this as we did in the previous illustration.

1986_Determine the solution to initial value problem.png

Yet again, we can drop the absolute value bars as we are squaring the term.

Here multiply the differential equation through the integrating factor as again, ensures it's the rewritten one and not the original differential equation.

(t-2 y)' = t2 sin(2t) - 1 + 4t

Posted Date: 4/10/2013 3:49:07 AM | Location : United States







Related Discussions:- Determine the solution to initial value problem, Assignment Help, Ask Question on Determine the solution to initial value problem, Get Answer, Expert's Help, Determine the solution to initial value problem Discussions

Write discussion on Determine the solution to initial value problem
Your posts are moderated
Related Questions
#question.I headed into Target in Webster, NY for an advertized free Earth Day Bag in (local newspaper and on your entrance store doors) and at 10:30 a.m. on Sunday, April 22nd, th

A group of 120 men had food for 200 days.After 5 days , 30 men die of disease.How long will the remaining food last

The radius of the in circle of a triangle is 4cm and the segments into which one side is divided by the point of contact are 6cm and 8cm.  Determine the other two sides of the tria

How to Make Equations of Conics Easier to Read ? If you want to graph a conic sections, first you need to make the equation easy to read. For example, say you have the equatio

E 1) Try the two activities detailed above with a few children around you Evaluate whether they really helped to improve the children's performance of mental arithmetic. Anot

The total ticket sales for a soccer game were $1,260; 210 tickets were purchased. If all the tickets are the similar price, what was the cost of a ticket? Divide the total sale

Danielle requires knowing the distance around a basketball court. What geometry formula will she use? The perimeter of a rectangle is two times the length plus two times the wi

Binormal Vector - Three Dimensional Space Next, is the binormal vector.  The binormal vector is illustrated to be, B → (t) = T → (t) * N → (t) Since the binormal vecto

Estimation of difference among population proportions Assume the two proportions be described by P1 and P2, respectively,Then the difference absolute between the two proportion