Q12 of 76 Page 929

Find the general solution of each of the following differential equations:

cos x(1 + cos y)dx – sin y(1 + sin x)dy = 0


Rearranging the terms we get:



Integrating both the sides we get:



⇒log|1 + sinx| = - log|1 + cosy| + logc


⇒log|1 + sinx| + log|1 + cosy| = logc


⇒(1 + sinx)(1 + cosy) = c


Ans: (1 + sinx)(1 + cosy) = c


More from this chapter

All 76 →
10

Find the general solution of each of the following differential equations:

ex tan y dx + (1 – ex) sec2 y dy = 0


 11

Find the general solution of each of the following differential equations:

sec2x tan y dx + sec2y tan x dy = 0


 13

For each of the following differential equations, find a particular solution satisfying the given condition :

.. where a ∈ R and y = 2 when x = 0.


 14

For each of the following differential equations, find a particular solution satisfying the given condition :

it being given that y = 1 when x = 0.