Q10 of 76 Page 929

Find the general solution of each of the following differential equations:
e^x tan y dx + (1 – e^x) sec² y dy = 0

Rearranging all the terms we get:

Integrating both the sides we get:

⇒log|1 - e^x| = log|tany| - logc

⇒log|1 - e^x| + logc = log|tany|

⇒tany = c(1 - e^x)

Ans: tany = c(1 - e^x)

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

sec²x tan y dx + sec²y tan x dy = 0

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

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

Find the general solution of each of the following differential equations:ex tan y dx + (1 – ex) sec2 y dy = 0