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Find the general solution of the differential equation d^2y/dx^2 - 5*dy/dx + 4y = 2x

Solve complimentary function: Let y = e^mxthen,
d²y/dx² - 5dy/dx + 4y = 0
m²e^mx - 5me^mx + 4e^mx = 0 (substituting fo...

Answered by Peter M. • Further Mathematics tutor

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In simple harmonic motion, where would the object have the largest speed. If the angular velocity is 2 rad s^-1, and the amplitude is 1m, what is the largest speed obtained by the object?

The largest speed is obtained at the position of equilibrium.

v=Aw

So v= 2 x 1

v=2ms^-1

Answered by William C. • Further Mathematics tutor

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A curve is mapped by the equation y = 3x^3 + ax^2 + bx, where a is a constant. The value of dy/dx at x = 2 is double that of dy/dx at x = 1. A turning point occurs when x = -1. Find the values of a and b.

^dy/_dx = 9x^2 + 2ax + b

x = 2, ^dy/_dx = 9(2)^2 + 2a(2) + b = 36 + 4a + b

x = 1, ^dy/_dx = 9(1)^2 + 2a(1) + b = 9 + 2a + b

Answered by Alistair R. • Further Mathematics tutor

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How do I know when I should be using the Poisson distribution?

To identify a Poisson distribution question, remember that in a Poisson distribution... Events occur independently of each other Events occur at a constant rate Events occur singly (that is, two can't hap...

Answered by Hannah D. • Further Mathematics tutor

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Why does matrix multiplication seem so unintuitive and weird?!

You're right, when you first learn about matrix multiplication it definitely doesn't feel like the easiest way of defining a form of multiplication. This is particularly true if you've just lear...

Answered by Daniel C. • Further Mathematics tutor

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