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2132worksheet1

2132worksheet1 - Your signature(4 Consider the...

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Polytechnic Institute of NYU MA 2132 Worksheet 1 Date: Print Name: Signature: ID #: Instructor: Jacobovits Problem Possible Points 1 12 2 16 3 16 4 20 5 16 6 20 Total 100

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Your signature: (1) Consider the differential equation x 3 [( x - 5) dy dx + y ] = x - 10 . (a) Given that C is a real constant and y = y ( x ), show that y = C x - 5 - 1 x 2 is a solution to the d.e. (b) If y (3) = - 4, find C and the maximal x -interval of existence of y . (c) If y (6) = 1, find C and the maximal x -interval of existence of y .
Your signature: (2) Consider the differential equation dy dx = y 4 x 2 + x . Solve the differential equation for an explicit solution for y .

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Your signature: (3) Consider the differential equation dx dt = 6 e 2 t - x . (a) Solve the differential equation for an explicit solution for x . (b) If x (0) = 0, solve the initial value problem.

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Unformatted text preview: Your signature: (4) Consider the diﬀerential equation 2 xy dy dx = 4 x 2 + 3 y 2 , x > . (a) Use a change of variables to convert the d.e. so that it is separable. You must express the answer in the form f ( u ) du = g ( x ) dx or p ( y ) dy = q ( x ) dx . (b) Solve explicitly for y . Your signature: (5) Solve the following initial value problem: dy dx =-x 2 + y cos( x ) sin( x ) + y , y (0) =-1 . Your signature: (6) Consider the diﬀerential equation ( x 2 + xy 2 ) y-3 xy + 2 y 3 = 0 . (a) Show that the d.e. is not exact. (b) Show that xy-2 is an integrating factor. (c) Solve the resulting d.e....
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2132worksheet1 - Your signature(4 Consider the...

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