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Q. If y=cot x, show that ```(d^2y)/dx^2` + 2y `dy/dx` = 0

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user8235304 | Student, Grade 11 | Valedictorian

Posted June 27, 2013 at 4:35 PM via web

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Q. If y=cot x, show that ```(d^2y)/dx^2` + 2y `dy/dx` = 0

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted June 27, 2013 at 4:43 PM (Answer #1)

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Given y=cotx

Then `(dy)/(dx)=-csc^2x`

and `(d^2y)/(dx^2)=-2cscx(-cscxcotx)=2csc^2xcotx`

So `(d^2y)/(dx^2)+2y(dy)/(dx)`

`=2csc^2xcotx+2cotx(-csc^2x)`

=0 as required.

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