Problem: Solving differential equation
Then by chain rule,
Rewrite (1) as
Integrate (3) with respect to gives
where since .
Square (4) gives
Solving for from (5), we obtain
Integrate (6) with respect to yields
since is an even function.
By definition (see “Deriving Two Inverse Functions“),
From “Integration of Trigonometric Expressions ” :
Without using a CAS,
Exercise-1 What is the derivative of hint: