100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
APM 2611- DIFFERENTIAL EQUATIONS-2019 $5.50   Add to cart

Exam (elaborations)

APM 2611- DIFFERENTIAL EQUATIONS-2019

 2 views  0 purchase
  • Course
  • Institution

APM 2611- DIFFERENTIAL EQUATIONS-2019

Preview 3 out of 18  pages

  • September 23, 2022
  • 18
  • 2022/2023
  • Exam (elaborations)
  • Questions & answers
avatar-seller
lOMoARcPSD|12263423




APM2611/201/1/2019




APM 2611- DIFFERENTIAL EQUATIONS-2019




Tutorial letter 201/1/2019


DIFFERENTIAL EQUATIONS
APM2611

Semester 1


Department of Mathematical Sciences


This tutorial letter contains solutions for assignment 01.




Downloaded by Anna Maina (annamurugijoe@gmail.com)

, lOMoARcPSD|12263423




BARCODE




Downloaded by Anna Maina (annamurugijoe@gmail.com)

, lOMoARcPSD|12263423




Question 1


(1.1) Find an interval of definition for the equation

dx
x2 = 3x3t2.
dt
Since the equation has the solution x(t) = 0 for all t, any interval may be taken as an interval
of definition. The largest interval of definition is (−∞, ∞).

(1.2) Solve the initial value problem
dx
x2 = 3x3t2, x(0) = 1
dt
and give an interval of definition.
Notice that x = 0 is a solution for the equation, but does not satisfy the initial value problem.
The equation is separable, separating variables yields
dx
= 3t2 dt.
x
Integrating both sides yields
ln |x| = t3 + c
where c is the constant of integration. Since x(0) = 1

ln |1| = 03 + c

we have c = 0. Thus
3
ln |x| = t3 ⇒ |x| = et .

Since x(0) = 1 (which is positive), and by continuity of x(t)
3
x = et .

Since the solution is valid for all t, an interval of definition is (−∞ , ∞ ) or any other interval
which contains the initial value 0.




2

Downloaded by Anna Maina (annamurugijoe@gmail.com)

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller Studiespro. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $5.50. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

67474 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling
$5.50
  • (0)
  Add to cart