How to you find the general solution of dy/dx=tan^2x?

Gretchen Allison

Gretchen Allison

Answered question

2022-09-11

How to you find the general solution of d y d x = tan 2 x ?

Answer & Explanation

SlowlFeet45

SlowlFeet45

Beginner2022-09-12Added 11 answers

We have
d y d x = tan 2 x
This is a First Order separable Differential Equation, so we can just collect terms in y, and terms in x and "separate the variables" to get:
  d y =   tan 2 x   d x
We can now integrate, and deal with the RHS integral by using the trig identify tan 2 θ = sec 2 θ - 1 , so we get:
          y =   ( sec 2 x - 1 )   d x
y = tan x - x + C , (where C is an arbitrary constant).

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