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solve dy/dx = y(sec x)^2

Firstly, this differential equation should be solved using the separation of variables method, where all y terms are moved the left hand side of the equation and all x terms are moved to the right hand side. In this case, dividing both sides by y results in the equation (1/y)dy/dx = (sec x)^2. Then to find y, both sides should be integrated with respect to x, so that ∫(1/y)dy = ∫(sec x)^2 dx. The integral of 1/y with respect to y is ln y, the natural logarithm of y, and and the integral of (sec x)^2 with respect to x is tanx. Also, an arbitrary constant must be added. The resultant equation is ln y = tan x + c. This can be written explicitly in terms of y where y = e^(tan x + c) or y = Ae^(tanx) where A = e^c, another arbitrary constant.

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