In Problems 1 and 2, y = 1/(1 + cje ) is a one-parameter family of solutions of the first-order DE y' = y – y. Find a solution of the first-order IVP consisting of this differential equation and the given the second-order IVP consisting of this differential equation and the given initial conditions. 7. x(0) = -1, x'(0) = 8 initial condition. 8. x(7/2) = 0, x'(7/2) = 1 1. y(0) = - 2. y(-1) = 2 (π/ )-0 9. x(π/6)-, In Problems 3-6, y = 1/(x + c) is a one-parameter family of so- lutions of the first-order DE y' + 2ry = 0. Find a solution of the 10. x(7/4) = V2, x'(T/4) = 2V2 In Problems 11–14, y = cje' + cze* is a two-parameter family of first-order IVP consisting of this differential equation and the given initial condition. Give the largest interval I over which the solution is defined. solutions of the second-order DE y" - y = 0. Find a solution of the second-order IVP consisting of this differential cquation and the given initial conditions. 3. y(2) = 4. y(-2) = 1 11. y(0) = 1, y'(0) = 2 6. y() = 5. y(0) = 1 = -4 12. y(1) = 0, y'(1) = e 13. y(-1) = 5, y'(-1) = -5 In Problems 7-10, x = e, cos t+ c2 sin t is a two-parameter family of solutions of the second-order DE x" +x = 0. Find a solution of 14. y(0) = 0, y'(0) = 0

Question

#7 

In Problems 1 and 2, y = 1/(1 + cje ) is a one-parameter family
of solutions of the first-order DE y' = y – y. Find a solution of the
first-order IVP consisting of this differential equation and the given
the second-order IVP consisting of this differential equation and the
given initial conditions.
7. x(0) = -1, x'(0) = 8
initial condition.
8. x(7/2) = 0, x'(7/2) = 1
1. y(0) = -
2. y(-1) = 2
(π/ )-0
9. x(π/6)-,
In Problems 3-6, y = 1/(x + c) is a one-parameter family of so-
lutions of the first-order DE y' + 2ry = 0. Find a solution of the
10. x(7/4) = V2, x'(T/4) = 2V2
In Problems 11–14, y = cje' + cze* is a two-parameter family of
first-order IVP consisting of this differential equation and the given
initial condition. Give the largest interval I over which the solution
is defined.
solutions of the second-order DE y" - y = 0. Find a solution of the
second-order IVP consisting of this differential cquation and the
given initial conditions.
3. y(2) =
4. y(-2) = 1
11. y(0) = 1, y'(0) = 2
6. y() =
5. y(0) = 1
= -4
12. y(1) = 0, y'(1) = e
13. y(-1) = 5, y'(-1) = -5
In Problems 7-10, x = e, cos t+ c2 sin t is a two-parameter family
of solutions of the second-order DE x" +x = 0. Find a solution of
14. y(0) = 0, y'(0) = 0

Image Transcription

In Problems 1 and 2, y = 1/(1 + cje ) is a one-parameter family of solutions of the first-order DE y' = y – y. Find a solution of the first-order IVP consisting of this differential equation and the given the second-order IVP consisting of this differential equation and the given initial conditions. 7. x(0) = -1, x'(0) = 8 initial condition. 8. x(7/2) = 0, x'(7/2) = 1 1. y(0) = - 2. y(-1) = 2 (π/ )-0 9. x(π/6)-, In Problems 3-6, y = 1/(x + c) is a one-parameter family of so- lutions of the first-order DE y' + 2ry = 0. Find a solution of the 10. x(7/4) = V2, x'(T/4) = 2V2 In Problems 11–14, y = cje' + cze* is a two-parameter family of first-order IVP consisting of this differential equation and the given initial condition. Give the largest interval I over which the solution is defined. solutions of the second-order DE y" - y = 0. Find a solution of the second-order IVP consisting of this differential cquation and the given initial conditions. 3. y(2) = 4. y(-2) = 1 11. y(0) = 1, y'(0) = 2 6. y() = 5. y(0) = 1 = -4 12. y(1) = 0, y'(1) = e 13. y(-1) = 5, y'(-1) = -5 In Problems 7-10, x = e, cos t+ c2 sin t is a two-parameter family of solutions of the second-order DE x" +x = 0. Find a solution of 14. y(0) = 0, y'(0) = 0

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