Q. 265.0( 1 Vote )

Solve: dy = cosx (2 – y cosecx)dx.

Answer :

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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