Q. 235.0( 3 Votes )

# <span lang="EN-US

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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