Problem Set 4(1) - 6 y” 8y’ – 9y = 0 y(1 = 1 y’(1 = 0 7 4y”-y=0 y-2)=1 y’-2)=-1 8 Find a differential equation whose general solution

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PROBLEM SET 4 1. Indicate if the equation is exact or not. If it is exact, find the solution. a) e y d x + (xe y – siny) d y = 0 b) (9x 2 + y –1) d x – (4y – x) d y = 0 , y(1)=0 c) (x + y) d x – x d y = 0 d) y’ = g G – ±²g ³g´µ² ·µ²g e) d x + (x/y – siny) d y = 0 For problems 2 through 4, find the general solution of the differential equation. 2. y” + 4y’ + 4y = 0 3. y” – 5y = 0 4. y” - y’ – 2y = 0 For problems 5 through 7, find the solution to the initial value problem. 5. 6y” – 5y’ + y = 0 y(0) = 4, y’(0) = 0
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Unformatted text preview: 6. y” + 8y’ – 9y = 0 y(1) = 1 y’(1) = 0 7. 4y”-y=0 y(-2)=1 y’(-2)=-1 8. Find a differential equation whose general solution is y = c 1 e 2t + c 2 e-3t 9. Find the solution of the initial value problem 2y”-3y’+y=0, y(0)=2, y’(0)=1/2. Then determine the maximum value of the solution and also find the point where the solution is zero. 10. Solve the initial value problem y”-y’-2y=0, y(0) = a, y’(0) = 2. Then find “a” so that the solution approaches zero as t b ∞...
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This note was uploaded on 12/08/2011 for the course M 427K taught by Professor Fonken during the Spring '08 term at University of Texas at Austin.

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