r taking Differential Equations, you have become a tutor. During your shift, a s

Question

r taking Differential Equations, you have become a tutor. During your shift, a student asks you to A semester afte check their solution to a second order, linear, homogeneous differential equation with constant coefficients. The problem also states two initial conditions. Determin correct, explain why. If they cannot be correct, explain certain vector spaces and their dimensions. e whether the answers below may be correct. If they may be why. Your explanations should contain thoughts about (a) The general solution to this problem is y(t) = C1 et + c2e2t (b) The fundamental solution set is (e,e2) (o) The solution to the initial value problem is yt) -e 2

Explanation / Answer

No, the answer is not correct. There is problem in part (c) of the answer. As solution given in part (c) is the general solution. It is not a solution of intial value problem as solution in part (c) has arbitrary constants c1 and c2, while these constants are part of general solution not particular solution.

Part (a) and part (b) are correct since it a differential equation of order 2 so its solution space will be of dimension 2. Thus general solution will be a linear combination of two linearly independent functions which spans the solution space. Functions given in the fundamental solution set are linearly independent and spans solution space. So part (a) and part (b) are correct, but part (c) is incorrect.

Therefore, answer is incorrect.

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