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Forced vibration:

The object oscillating will vibrate upwards and downwards with the same frequency the driving oscillation is at. The amplitude of the v...

Both diamond and graphite are made of carbon. Carbon can form a maximum of 4 covalent bonds due to carbon having 4 electrons on it's outer shell. In diamond, each carbon atom forms 4 covalent bonds in ...

Speed is a scalar quantity, meaning that it only has a magnitude. Acceleration is a vector quantity, meaning that it has a magnitude and a direction. Velocity is the vector quantity equivalent of speed...

we can use the subtraction method to find this out:

create a table set out like this

  2⁷  |  2⁶  |  2⁵  |  2⁴  |  2³ ...

Divide through by x so:      (dy/dx) +2(y/x) = 4x

Now multiply through by the intergrating factor:  e^(| (2/x) dx) = e^(2.ln(x)) = x^2

so you get:     (x^2)(dy/dx) + 2xy = 4...