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:

A similar problem is given at

answer is 67%

step-by-step explanation:

hi there!

first we need to find out how much they are adding to each number to make the next number.

ex: 4 + 4 = 8, 8 + 8 = 16, and so on.

so continuing with 32,

32 + 32 = 64

64 + 64 = 128

128 + 128 = 256

256 + 256 = 512

4, 8, 16, 32, 64, 128, 256, 512

the 8th term of the sequence will be 512

hope this ! ~