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Tutor profile: Bruce C.

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Bruce C.
Graduate Student and NASA Scientist
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Questions

Subject: Calculus

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Question:

What is the partial derivative with respect to x of the following expression, $(yxcos(ax)$)

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Bruce C.
Answer:

Since this is a partial derivative we treat all variables other than x as a constant. We then have two parts with x in them, and apply the product rule to each component. $(ycos(ax) - yxasin(ax)$)

Subject: Aerospace Engineering

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Question:

If there is no circulation in a fluid flow, what is the vorticity at any point in the flow?

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Bruce C.
Answer:

By the definition of circulation, $$\Gamma$$, the vorticity is zero at all points in the flow.

Subject: Differential Equations

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Question:

Find the general solution, $$y(x)$$.$( y'' - 4y' +4y' = 0$)

Inactive
Bruce C.
Answer:

This is a second order linear homogeneous differential equation, so we can solve easily by finding the roots of the auxiliary equation. This has roots in the form, $(m^2-4m+4=(m-2)(m-2) $) Because there are identical repeat roots, the complimentary solution is in the form, $( y_c=c_1e^{2x} + c_2xe^{2x}$)

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