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MTH401 Spring 2012 Assignment #02: Solving Diff. Equations, Exercises of Mathematics

Instructions and two problems for an assignment in a mathematics course (mth401) during spring 2012. Students are required to find the solutions of given homogeneous and nonhomogeneous differential equations using the methods of reduction of order and undetermined coefficients-superposition approach. The document also includes a hint for handling jump discontinuities in the function p(x).

Typology: Exercises

2011/2012

Uploaded on 08/03/2012

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Assignment # 02
MTH401 (Spring 2012)
Total marks: 30
Lecture # 12-18
Due date: 08-05-2012
DON’T MISS THESE Important instructions:
Upload assignments properly through LMS only, (No Assignment will be
accepted through email).
All students are directed to use the font and style of text as is used in this
document.
In order to attempt this assignment you should have full command on
Lecture # 12 to Lecture # 18.
This is an individual assignment, not group assignment, so keep in mind that you
are supposed to submit your own, self made & different assignment even if you
discuss the questions with your class fellows. All similar assignments (even with
some meaningless modifications) will be awarded zero marks and no excuse will
be accepted. This is your responsibility to keep your assignment safe from others.
Above all instructions are for all assignments so may not be mentioned in future.
Solve the assignment on MS word document and upload your word (.doc) files only. Do
not solve the assignment on MS excel. If we get any assignment on MS excel or any
format other than word file then it will not be graded.
Assignments through e-mail are not acceptable after due date (If there is any
problem in submitting your assignment through LMS, you can send your solution
file through email with in due date). You are advised to upload your assignment
at least two days before Due date.
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Download MTH401 Spring 2012 Assignment #02: Solving Diff. Equations and more Exercises Mathematics in PDF only on Docsity!

Assignment # 02

MTH401 (Spring 2012)

Total marks: 30 Lecture # 12- Due date: 08-05-

DON’T MISS THESE Important instructions:

 Upload assignments properly through LMS only, (No Assignment will be accepted through email).  All students are directed to use the font and style of text as is used in this document.  In order to attempt this assignment you should have full command on Lecture # 12 to Lecture # 18.  This is an individual assignment, not group assignment, so keep in mind that you are supposed to submit your own, self made & different assignment even if you discuss the questions with your class fellows. All similar assignments (even with some meaningless modifications) will be awarded zero marks and no excuse will be accepted. This is your responsibility to keep your assignment safe from others.  Above all instructions are for all assignments so may not be mentioned in future.  Solve the assignment on MS word document and upload your word (.doc) files only. Do not solve the assignment on MS excel. If we get any assignment on MS excel or any format other than word file then it will not be graded.  Assignments through e-mail are not acceptable after due date (If there is any problem in submitting your assignment through LMS, you can send your solution file through email with in due date). You are advised to upload your assignment at least two days before Due date.

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Question#1 Marks 10

In the following differential equation the indicated function y 1  x  is a solution of the

associated homogeneous equation. Use the method of reduction of order to find a second

solution y 2  x  of the homogeneous equation and a particular solution of the given

nonhomogeneous equation using method of undetermined coefficients-superposition approach.

1

2 2 2 4 2 ;^

d y (^) y y e x dx

  ^ 

Question#2 Marks 20

Solve the following initial value problem.

dy p x y y dx

Where

x p x x

^ ^ 

Hint:

Linear differential equations sometimes occur in which the function p  x  have

jump discontinuities. If x 0 is such a point of discontinuity, then it is necessary to solve

the equation separately for x  x 0 and x  x 0. Afterwards, the two solutions are

matched so that the function y  x is continuous at x 0 ; this is accomplished by a proper

choice of the arbitrary constants.

In the given differential equation p  x  has a jump discontinuity at x 0  1 , then it is

necessary for all of you to solve the equation separately for x  1 and x  1.

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