Question

sin xdy/dx+ 2y + sin x (1 + cos x) = 0.
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Answer 1

Answer:

Rearranging the terms,

dy/dx +(2/sinx) y = -(1+cosx)

Q=-(1+cosx)

This is linear differential equation.

integrating factor =>IF=e^(int 2/sinx)

After solving , IF= 1/(cosecx -cotx)^2

You can even simplify above IF term.

Now solution,

y IF =int (Q IF )dx +c

Solve the above equation and you get the answer.

Hope this will help. Sorry for not providing entire answer as I m typing this answer in bus.

Happy Learning!