Can someone solve this? :)

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1 Answer
May 13, 2018

This is a first order linear differential equation

Explanation:

Start off by rearranging the equation. Get the dxdy or dydx on one side and the other terms on one side.

In this question we rearrange the equation by getting dxdy on one side. After splitting the numerator and solving , we get ,

dxdy + xy1+y2 = siny1+y2

-> This is a linear differential equation of the type
dxdy + Px = Q
(Here P and Q are functions of y)
In this equation P = y1+y2

The integrating factor for the equation is :
-> e(Pdx)
->e(ydy1+y2)
->Solving the integral using substitution
-> Let 1+y2 = t
->Upon differentiating , you get , ydy=dt2
You end up with e12(log(1+y2))
Integrating factor is ->1+y2**

Multiplying this factor on both sides and then integrating ,

-> x.1+y2 = (siny1+y2).1+y2
Cancelling 1+y2 you get ,

x.1+y2 = (sinydy)
Upon integrating ,
x.1+y2 = cosy+C

Therefore the final answer is :
-> x.1+y2 + cosy = C