Question

Solve:
( sec x ) dy/dx = y + sin x
The answer: y = Cesin x – ( 1 + sin x )

Answer 1

Final Answer :
$y = c {e}^{ \sin(x) } - (1 + \sin(x) ) \\ where \: c \: is \: arbitrary \: constant \:$

These Calculations include:
1) Solving First order linear Differential Equation.
2) Integration by Parts

Steps
1) Multiply by cos x in both sides :
Use : sec x * cos x = 1:

2) Find Integrating Factor :

e ^ (-sin x)

3) Multiply integrating factor into both sides :

4) Integrate in both sides

End :)
Hope, you umderstand my answer and it may helps you !!