Consider the differential equation: 2y′′−13y′−7y = 0 a. Show that, for any constants A and B, the following is a solution to the above differential equation: y = Ae^(−9x)+Be^(x/3)

b. Find the values A and B that make the above general solution into a solution for the following initial value problem: 2y′′−13y′−7y = 0; y(0) = 3, y′(0) = −5

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Just a correction, the characteristic roots of the equation are and , thus, we should test for:

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Question a:

, thus, we found the identity, and for each constant A and B, the following is a solution.

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Question b:

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Using

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Then, B is given by:

Thus, the values are:

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