Assignment_Questions [May 2014]
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ASSIGNMENT ORDINARY DIFFERENTIAL EQUATIONS [FDM 1023] 1. Solve the following differential equations. i) 0 1 1 2 2 2 2 2 = + + + + - + dy y x x ye dx y x y x x y , ii) 2 ' ' ' 1 2 x e y y y x + = + - , iii) 0 6 3 3 4 4 = + dx y d dx y d x . 2. Find the power series solutions around 1 0 - = x for the following differential equation ( ) 0 3 1 ' ' ' = - + + y xy y x . 3. Use the Laplace transform to solve the following differential equation ( ) t f y y = + ' ' , ( ) 0 0 = y , ( ) 1 0 ' = y where () ≥ < ≤ < ≤ = π π π π 2 , 0 2 , 1 0 , 0 t t t t f . 4. Sketch the graph of the following function and find its Fourier coefficients () < ≤ - < ≤ - - < ≤ - - = 4 2 5, 2 2 10, 2 4 5, x x x x f ( ) ( ) x f x f = + 8 , . Submission by group (4 - 5 students) Solutions must be HAND-WRITTEN. Submission date: August 20, 2014 (Wednesday) (Before 5pm at Level 3, Building 19) Please use the template (next page) as the Front Page of your assignment.
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Transcript of Assignment_Questions [May 2014]
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ASSIGNMENT
ORDINARY DIFFERENTIAL EQUATIONS [FDM 1023]
1. Solve the following differential equations.
i) 011 22222 =
+++
++ dy
yxxyedx
yxy
xx
y,
ii) 2''' 12 xeyyy
x
+=+ ,
iii) 06 33
4
4
=+dx
yddx
ydx .
2. Find the power series solutions around 10 =x for the following differential equation
( ) 031 ''' =++ yxyyx .
3. Use the Laplace transform to solve the following differential equation
( )tfyy =+'' , ( ) 00 =y , ( ) 10' =y where
( )
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ORDINARY DIFFERENTIAL EQUATIONS (FDM 1023)
MAY 2014
ASSIGNMENT
No. Name ID Program Signature 1.
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