Show that every separable equation of the form M(t)+ N(y)dy/dt=O is exact

Chapter 1, Problem 15

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QUESTION:

Show that every separable equation of the form M(t)+ N(y)dy/dt=O is exact.

Questions & Answers

QUESTION:

Show that every separable equation of the form M(t)+ N(y)dy/dt=O is exact.

ANSWER:

Step 1 of 2

The given differential equation is, . The objective is to prove that the equation is exact.

Multiply both sides of the given equation by .

                                     

The obtained equation is of the form .

Then, on comparing we get,  and .

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