2132worksheet2

# 2132worksheet2 - tions if possible(a 2 y 00 5 y-3 y = 0(b y...

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Polytechnic Institute of NYU MA 2132 Worksheet 2 Date: Print Name: Signature: ID #: Instructor: Jacobovits Problem Possible Points 1 10 2 8 3 10 4 10 5 24 6 16 7 14 8 8 Total 100

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Your signature: (1) Find the particular solution of the diﬀerential equation y 0 + (cos x ) y = cos x, y ( π ) = 0 .
Your signature: (2) Find the general solution of the diﬀerential equation ( x 2 + 1) y 0 - 2 xy = x 2 + 1 .

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Your signature: (3) Consider the diﬀerential equation 2 xy 0 + 3 y + x 4 y 3 = 0 . (a) Use a change of variables to convert the d.e. so that it is linear order one. You must express the answer in the form y 0 + p ( x ) y = q ( x ). (b) Find the general solution of the diﬀerential equation.
Your signature: (4) Find the general solution of the diﬀerential equation xy 0 - y + e x y 2 = 0 , x > 0 .

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Your signature: (5) Express the general solution of the given diﬀerential equation in terms of exponential func-

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Unformatted text preview: tions, if possible. (a) 2 y 00 + 5 y-3 y = 0 (b) y 000-4 y = 0 (c) y 00-20 y + 100 y = 0 Your signature: (6) For each of the following diﬀerential equations ﬁnd all numbers r , real and complex, such that e rx is a solution. Find all linearly independent real solutions. (a) y ” + 4 y + 5 y = 0 (b) y (5) + 4 y 000 = 0 Your signature: (7) Find the solution of the initial value problem y 00 + 2 y + 2 y = 0 , y (0) = 2 , y (0) =-3 Your signature: (8) Find the solution of the given system of diﬀerential equation. (a) y 00 + 2 y-3 y = 5 e 2 x ; y (0) = 5, y (0) = 2. (b) y 00 + 3 y + 2 y = 36 xe x . (c) y 00 + 3 y + 2 y = 20 cos 2 x ; y (0) =-1, y (0) = 6....
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2132worksheet2 - tions if possible(a 2 y 00 5 y-3 y = 0(b y...

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