Question

find integrating factor if the diffrential equation of dy/dx_ycosx=xcos x is....

​

Answer 1

Answer:

e ^ (- Sinx )

Step-by-step explanation:

Given----> dy/dx - y Cosx = x Cosx

To find---> Integrating factor of given differential equation.

Solution---> We know that linear differential equation in x is

dy/dx + P y = Q

Where P and Q , are function of x only.

Now , for solution of this type of differetial equation , we first find integrating factor

Integrating factor = e^ ( ∫ P dx )

And one more thing we must know that

e ^ ( logx ) = x

Now returning to original problem,

dy/dx - y Cosx = x Cosx

Comparing it with dy/dx + P y = Q , we get,

P = - Cosx , Q = x Cosx

Integrating factor = e ^ ( ∫ P dx )

= e ^( ∫ - Cos x dx )

= e ^ ( - Sinx )

#Answerwithquality&#BAL

Answer 2

$<font color =“orange”>$

${ \huge \bf{ \mid{ \overline{ \underline{Answer}}} \mid}}$

$\huge\underline{\underline{\texttt{\purple{ e^ (-sinx) }}}}$

#answerwithquality #bal