Q. 265.0( 1 Vote )

# Solve: dy = cosx (2 – y cosecx)dx.

Given, A differential equation dy = cosx (2 – y cosecx)dx

To find: Find the solution of the given differential equation.

Explanation: We have dy = cosx (2 – y cosecx)dx.

We can write as,  So,  ….(i)

Now, It is a form of the linear differential equation in the form, When comparing the equation (i) with a linear differential equation, we get

P = cot x and Q = 2cosx

Since, The solution of the Linear differential equation is

I.F = And,

I.F × y So, The solution for the given linear differential equation is

I.F I.F = elog sin x

I.F = sin x

Now, The general solution is

y. sin x Since, sin2x = 2sinx.cosx

y. sin x Let 2x = t

On differentiating this, we get

2 dx = dt y. sin x y. sin x substitute the value of t; we get

y. sin x Hence, This is the solution of given Linear differential equation.

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