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How to you find the general solution of #dy/dx=sin2x#?

Answer 1

Emilia Aguilar

Use the separation of variables method. Answer:
#y = -1/2cos(2x) + C#

#dy = sin(2x)dx#

#intdy = intsin(2x)dx#

#y = -1/2cos(2x) + C#

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Answer 2

Evelyn Agard

To find the general solution of ( \frac{dy}{dx} = \sin(2x) ), integrate both sides with respect to ( x ):

[ \int dy = \int \sin(2x) , dx ]

[ y = -\frac{1}{2} \cos(2x) + C ]

So, the general solution is ( y = -\frac{1}{2} \cos(2x) + C ), where ( C ) is the constant of integration.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.