Question

The general solution of e x cosydx−e x sinydy=0 is :__________

Answer 1

Answer:

General solution    x   = log | sec y | + C            

Step-by-step explanation:

Step(i):-

Given

          $e^{x} cosy dx - e^{x} sin y d y = 0$

         $e^{x} (cosy dx = e^{x} sin y d y$

           cos y dx = sin y d y

                $dx = tan y d y$

Step(ii):-

now integrating on both sides , we get

            $\int\limits {1} \, dx = \int\limits {tany} \, dy$

by using formula

               $\int\limits {tany} \, dy = log | sec y | + C$

             x   = log | sec y | + C

Final answer:-

General solution    x   = log | sec y | + C