100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
APM2611 Assignment 1 (COMPLETE ANSWERS) 2024 R50,44   Add to cart

Exam (elaborations)

APM2611 Assignment 1 (COMPLETE ANSWERS) 2024

 7 views  0 purchase

APM2611 Assignment 1 (COMPLETE ANSWERS) 2024 ;100 % TRUSTED workings, explanations and solutions. For assistance call or W.h.a.t.s.a.p.p us on ...(.+.2.5.4.7.7.9.5.4.0.1.3.2)...........

Preview 3 out of 22  pages

  • June 11, 2024
  • 22
  • 2023/2024
  • Exam (elaborations)
  • Questions & answers
book image

Book Title:

Author(s):

  • Edition:
  • ISBN:
  • Edition:
All documents for this subject (11)
avatar-seller
LIBRARYpro
APM2611
ASSIGNMENT 1 2024
UNIQUE NO.
DUE DATE: 8 MAY 2024

, APM2611/101/0/2024


ADDENDUM A: ASSIGNMENTS

ASSIGNMENT 01
Due date: Wednesday, 8 May 2024
-

ONLY FOR YEAR MODULE

First order separable, linear, Bernoulli, exact and homogeneous equations. Higher order
homogeneous DE’s. Solving non-homogeneous DE’s using the undetermined
coefficients, variation of parameters and operator methods.

Answer all the questions. Show all your own and personalized workings, you get ZERO
to a question if we see that you have copied someone’s else solution word by word.

If you choose to submit via myUnisa, note that only PDF files will be accepted.

Note that all the questions will be marked therefore, it is highly recommended to attempt all of them.

Question 1
Prove that the given function is a solution of the given differentialequation.
1.
y00− 2y 0 + 5y = 0 ; y = e x (cos 2x − sin 2x)

2.
dy π
− ecos x = −y cot x , y( ) = 4;
dx 2
y = − csc x(e cos x − 5)

3. (i) Verify that y = θ 1 (x) = x 2 and y = θ 2 (x) = −x 2 are solutions of the differential equation
xy 0 − 2y = 0 on the interval (−∞, ∞).
(ii) Verify that the piecewise-direction function
−x 2 , x<0
y= x 2, x≥0
is a solution of xy 0 − 2y = 0 on the interval (−∞, ∞).


Question 2
Consider the DE
(6xy − y 3)dx + (4y + 3x 2 − 3xy 2 )dy = 0.
1. Prove that it is exact.
2. Solve it.



11

, Question 3
Solve the following DEs:
1.
dy
x2 + 2xy = 5y 3
dx
2.
x 2 y0 = y 2
+ 2y + 1, y(1) = 13


Question 4

1. Solve the given differentialequations by separation of variables:
(i)
dy
ex y −y
= e + e−2x−y
dx
(ii)
2
dx y+1
y ln |x| =
dy x
2. Solve the initial value problem:
dy y2 − 1
= 2 , y(2) = 2
dx x −1
3. Solve the following DEs using the appropriate substitutions.
(a)
dy y
x = y + xe x , y(1) = 1
dx
(b)
xy − y 2
y0 = Hint: make substitution y = ux
x2 − y 2
Leave your answer in an implicit form.
(c)
x 2 y00+ 2xy 0 + y = 0


Question 5

1. A large tank is filled with 500 litres of pure water. Brine containing 2kg of salt per litre is
pumped into the tank at a rate of 5 litres/min. The well-mixed solution is pumped out at the
same rate. Find the number A(t) of kg of salt in the tank at time t. What is the concentration
of the solution in the tank at t = 5min?
2. Solve part (1.) under the assumption that the solution is pumped out at a faster rate of 10
litres/min. When is the tank empty?


– End of assignment –
12

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 EFT, 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 this summary from?

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

Will I be stuck with a subscription?

No, you only buy this summary for R50,44. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

71184 documents were sold in the last 30 days

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

Start selling
R50,44
  • (0)
  Buy now