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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 mx then, d 2 y/dx 2 - 5dy/dx + 4y = 0 m 2 e mx - 5me mx + 4e mx = 0 (substituting for y) e mx (m 2 - 5m + 4) = 0 e mx (m - 4)(m - 1) = 0 Therefore m=4 and m=1, so the ...
PM
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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
WC
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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 36 + 4a + b = 2(9 + 2a + b) b = 18 x = -1, dy / dx = 0 = 9(-1)^2 + 2a(-1) + 18 9 - ...
AR
3060 Views

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 happen...
HD
3450 Views

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 learned about add...
DC
19312 Views