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exercises-differential-equations

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

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Functions and their properties 1 Exercises: Differential Equations Solve the given first order linear equations and/or initial value prob- lems. If no initial value is given find its general solution. 1. y ( x ) + 2 y ( x ) = 4 x. Answer: Ce 2 x + 2 x 1, where C is a constant. 2. y (tan x ) y = sec x, y (0) = 0. Answer: y ( x ) = x sec x . 3. y ( x ) + 2 xy ( x ) = xe x 2 . Answer: e x 2 C + x 2 2 where C is a constant. 4. y + y = cos x. Answer: Ce x + 1 2 (cos x + sin x ) where C is a constant. 5. y + ay = e mx , where a, m are constants. Answer: y ( x ) = ( C + x ) e mx , if m = a, Ce x + e mx m + a , if m = a. 6. xy + y = e x , y ( a ) = b
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