exercises-differential-equations

exercises-differential-equations - Functions and their...

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Functions and their properties 1 Exercises: Diferential Equations Solve the given frst order linear equations and/or initial value prob- lems. IF no initial value is given fnd its general solution. 1. y 0 ( x )+2 y ( x )=4 x. Answer: Ce 2 x +2 x 1, where C is a constant. 2. y 0 (tan x ) y =sec x, y (0) = 0. Answer: y ( x )= x sec x . 3. y 0 ( x xy ( x xe x 2 . Answer: e x 2 ± C + x 2 2 ² where C is a constant. 4. y 0 + y =cos x. Answer: x + 1 2 (cos x +sin x )where C is a constant. 5. y 0 + ay = e mx , where a, m are constants. Answer: y ( x ( C + x ) e mx , if m = a, x + e mx m + a , if m 6 = a. 6. xy 0 + y = e x ,y ( a b ,( a 6 = 0) are given constants.
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This note was uploaded on 01/22/2011 for the course CS 225 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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