Find one-parameter families of solution curves of the following differential equations:
e–ysec2ydy = dx + xdy
e–ysec2ydy = dx + xdy
Given e–ysec2ydy = dx + xdy
This is a first order linear differential equation of the form
Here, P = 1 and e–ysec2y
The integrating factor (I.F) of this differential equation is,
We have
∴ I.F = ey [∵ elog x = x]
Hence, the solution of the differential equation is,
Recall
⇒ xey = tan y + c
∴ x = (tan y + c)e–y
Thus, the solution of the given differential equation is x = (tan y + c)e–y