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What is a solution to the differential equation #dy/dx=1/sec^2y#?

Answer 1

Cameron Alexander

#y = arctan(x+C)#

Grouping variables

#dy/cos^2y=dx# so

#tan y = x + C# so

#y = arctan(x+C)#

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Answer 2

Cameron Alexander

# y=tan^(-1)(x+C) #

# dy/dx = 1/sec^2y #

This is a first order separable Differential Equation; so we can "separate the variables" to give:

# int sec^2ydy = int1dx #

Integrating gives:

# tan y = x + C #, where #C# is the constant of integration Hence, the solution is:

# y=tan^(-1)(x+C) #

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Answer 3

Cameron Alexander

The solution to the differential equation ( \frac{dy}{dx} = \frac{1}{\sec^2(y)} ) is:

[ x = \tan(y) + 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.