Q. 235.0( 3 Votes )

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Answer :

Before starting solving the differential equation, we should know the type of differential equation.

This is the linear type differential equation,


– y = sinx


It is of the form + Py = Q where P and Q are either constants or function of x.


To solve these type of equations, we need to first find the integrating factor which is = and multiply both sides of the general form of equa the tion and after that integrate the whole equation.


First, convert the given equation in general form equation,


– y = sinx


P = - 1 and Q = sinx


Now find the I.F. = = e - x


Multiplying both sides by I.F. we get,


e - x – e - x y = e - x sinx


Integrating both sides with respect to x, we get,



e - x y + e - x y = (–1) e - x (cosx + sinx) + C


2 e - x y = (–1) e - x (cosx + sinx) + C


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