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Solve the second order differential equation d^2y/dx^2 - 4dy/dx + 5y = 15cos(x), given that when x = 0, y = 1 and when x = 0, dy/dx = 0

As we know, a general solution for a given differential equation is the complimentary solution + the particular solution/integral, this case is no different. To solve for the complimentary solution, form the...
AG
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A curve C has equation y = x^2 − 2x − 24 x^(1/2), x > 0. Find dy/dx and d^2y/dx^2. Verify that C has a stationary point when x = 4

Using the differentiation rule that d (Ax^b)/dx = Abx^(b-1) we find dy/dx = 2x -2 -12x^(-1/2).Similarly, taking care to see that the -2 term becomes zero since it is not dependent on x, we haved^2y/dx^2 = 2 ...
AW
2996 Views

Find all square roots of the number 3 + 4i.

To start we need to set up the equation described by the question. Our answers should be in the form a + bi (where a and b are real), and since any answers are the root of 3 + 4i we can write down the follow...
4368 Views

Find the volume of revolution formed by rotating the curve y = sinx 2pie around the x- axis

To solve this problem we need a formula. Integral of y 2 dx multiplied by pie. First we square the questions of the curve we are given (sinx) 2 . Next we apply double angle formula to reduce the power so we ...
AM
3736 Views

Explain the process of using de Moivre's Theorem to find a trigonometric identity. For example, express tan(3x) in terms of sin(x) and cos(x).

Identify de Moivre's Theorem: (cos(x) + isin(x)) n = cos(nx) + isin(nx) 2) Deduce the correct value of n for the given problem. In this example we set n=3 3) Expand the LHS (usually by a binomial expansion)....
OL
5338 Views