Question

What are all solutions to the differential equation dy/dx=sec^2*x ?

Options:

y=tanx+C
y=secx+C
y=1/3sec^3*x+C
y=2sec^2*xtanx+C

Answer 1

y=tanx+C

Explanation:

`(dy)/(dx) = {sec}^(2) \: x \\ \\ dy = {sec}^(2) \: x \: dx \\ integrating \: both \: sides \\ \\ \int \:1\: dy = \int {sec}^(2) \: x \: dx \\ \\ \huge \red{ \boxed{ \therefore \: y = tan \: x + c}} \\`