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# Tutor profile: Bruce C.

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Bruce C.
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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.

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.

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\$)

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Bruce C.

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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