FizeauV

2021-03-06

Give the correct answer and solve the given equation

Arnold Odonnell

Skilled2021-03-07Added 109 answers

We will first write this equation as

Notice that

means that

not a solution of the given equation.

Thus,

by

Make the substitution

(use the Chain Rule). Furthermore, (2) becomes

Combining (3) and (4), we get

Notice that this is a separable equation! It can be written as

Integrate both sides:

Clearly,

where

For the other integral, we use the integration by parts:

where

(In last equality we need used that

and the property of the logarithmic function:

Finnaly. (5) becomes

where

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