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For a homogeneous second order differential equation, why does a complex conjugate pair solution (m+in and m-in) to the auxiliary equation result in the complementary function y(x)=e^(mx)(Acos(nx)+Bisin(nx)), where i represents √(-1).

For a second order differential equation, our auxiliary equation, am 2 +bm+c=0, has two roots. Let's denote these roots as A and B. Note that A and B can be the same if there is a repeated root, but we're no...
JB
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State the conditions by which a Poisson distribution model may be suitable for a given random variable X.

The events recorded by X occur randomly, independently, singly in space and time and at a constant average rate (an average (mean) rate proportional to the length of the interval).
KC
2692 Views

How do I integrate arctan(x) using integration by parts?

This is an example where we use integration by parts, but it is not immediately obvious where to start.Recall the integration by parts formula ∫u(dv/dx) dx = uv - ∫(du/dx)v dx KEY STEP: We write arctan(x) = ...
OC
24373 Views

Integrate xsin(x).

The technique we need to use to solve this integral is called integration by parts. The parts formula is: the integral of (uv' dx) = uv - the integral of (u'v dx) (where u and v are functions of x). We need ...
JW
3144 Views

'Find the first derivative, with respect to x, of arctan(1/x) for non-zero real x. Hence show that the value of arctan(x)+arctan(1/x) is constant for all non-zero x, explicitly stating this constant in your final answer.' How do I solve this?

I have linked the solution to this problem here. https://www.icloud.com/iclouddrive/0mLKDeFREhbvTJm6D09jFakcw#Solution
3086 Views