Question

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

Answer 1

General solution x = log | sec y | + C

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