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

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Answer 1 · 2016-10-20T21:56:19

# 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) #

Answer 2 · 2016-10-20T21:58:03

#y = arctan(x+C)#

Grouping variables

#dy/cos^2y=dx# so

#tan y = x + C# so

#y = arctan(x+C)#