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dy/dx = -3 +12x^-4 d^2y/dx^2 = -48x^-5

cos(theta)-(4/3)cos³(theta)

a) What can we find from what we have been given?

dx/dt and dy/dt

How can we relate these values to dy/dx?

In the context of equations that only contain two variables, their derivativ...

Intergrating with respect to time, you get that v = u + at. Knowing that velocity is just the rate of change of your position ds/dt = v, and sustituting the previous expression for v, you get ds/dt = u + ...

We begin by quoting the integration by parts formula, as the question speciaficaly asks us to use it.

integrate(u(x) v'(x) dx)|^(b)(a) = [u(x) v(x)]^(b)(a) - integrate(u'(x) v(x) dx)|^(b)_...