Your last submission is used for your score. 1. [-/1 Points] DETAILS MY NOTES ZILLDIFFEQMODAP11 1.2.011. In this problem, $y = c_1e^x + c_2e^{-x}$ is a two-parameter family of solutions of the second-order given initial conditions. y(0) = 1, y'(0) = 4 y =
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We need to find the values of cā and cā that satisfy the initial conditions y(0) = 1 and y'(0) = 4. Show moreā¦
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EXERCISES 4.1 4.1.1 Initial-Value and Boundary-Value Problems In Problems 1ā4 the given family of functions is the general solution of the differential equation on the indicated interval. Find a member of the family that is a solution of the initial-value problem. 1. y = c1 e^x + c2 e^{-x}, (-ā, ā); y'' - y = 0, y(0) = 0, y'(0) = 1 2. y = c1 e^{4x} + c2 e^{-x}, (-ā, ā); y'' - 3y' - 4y = 0, y(0) = 1, y'(0) = 2 3. y = c1 x + c2 x ln x, (0, ā); x^2 y'' - x y' + y = 0, y(1) = 3, y'(1) = -1 4. y = c1 + c2 cos x + c3 sin x, (-ā, ā); y''' + y' = 0, y(Ļ) = 0, y'(Ļ) = 2, y''(Ļ) = -1
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Verify that the Indicated family of functions is a solution of the given differential equation. Assume appropriate interval of definition for each solution: y = C1e^x + C2e^3x + C3e^(8r) + C4e^(3r) Thus, the family of functions is given by: y = C1e^x + C2e^3x + C3e^(8x) + C4e^(3x)
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