[SOLUTION] The Characteristic Polynomial

Consider the BVP for the function y given byy??+ 25 y = 0, y(0) = 4, y (?5) = 5.(a) Find r1, r2, roots of the characteristic polynomial of the equation above.r1,r2 =(b) Find a set of real-valued fundamental solutions to the differential equation above.y1(x) =y2(x) =(c) Find all solutions y of the boundary value problem.y(x) =Note 1: If there are no solutions, type No Solution. Note 2: If there are infinitely many solutions, use k for the arbitrary constant.See in LN, § 6.1, See Examples 6.1.2-6.1.3. 2. (10 points)Consider the BVP for the function y given byy??+ 36 y = 0, y(0) = 1, y(?) = 1.(a) Find r1, r2, roots of the characteristic polynomial of the equation above.r1,r2 =(b) Find a set of real-valued fundamental solutions to the differential equation above.y1(x) =y2(x) =(c) Find all solutions y of the boundary value problem.y(x) = 1Note 1: If there are no solutions, type No Solution. Note 2: If there are infinitely many solutions, use k for the arbitrary constant.

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[SOLUTION] The Characteristic Polynomial
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