Home
Class 12
MATHS
The solution of differential equation (d...

The solution of differential equation `(dy)/(dx)+(y)/(x)=sin x` is

A

`x(y+cos x)=sin x+C`

B

`x(y-cos x)=sin x+C`

C

`xy cos x=sin x+C`

D

`x(y+cosx)=cos +C`

Text Solution

Verified by Experts

The correct Answer is:
B
Given differential equation is `(Dy)/(dx+y(1)/(x)=sinx`
which is linear differential equation.
Here, `P=(1)/(x)and Q=sin x`
`therefore IF=e^(int(1)/(x)dx)=e^(logx)=x`
The general solution is `y.x.=intx.sin xdx+C`
`"Take" I=intx sin xdx`
`-x cos x -f -cos xdx`
`-x cos x+sin x`
Put the value l in Eq. (i), we get
`xy=-x cos x+sin x+C`
`Rightarrow x(y+cos x)=sin x+C`
Promotional Banner

Similar Questions

Explore conceptually related problems

The solution of differential equation x(dy)/(dx)=y is :

solution of differential equation (dy)/(dx)=(y-x)^(2) is:

The solution of differential equation x(dy)/(dx)+y=x^(3) is :

IF the solution of differential equation ( dy)/(dx) = ( x-y) /( x+y) is ( x+ y )^2= C + a x ^2 then a is ____

The solution of the differential equation (dy)/(dx)=(x-y)/(x-3y) is (where, c is an arbitrary constant)

The solution of the differential equation (dy)/(dx)=(x-y)/(x+4y) is (where C is the constant of integration)

The solution of differential equation cos x (dy)/(dx)+y sin x =1

The solution of the differential equation (dx)/(x)+(dy)/(y)=0 is

The solution of the differential equation (dy)/(dx)=(2x-y)/(x-6y) is (where c is an arbitrary constant)

Find the general solution of the differential equation (dy)/(dx) = (y)/(x) + cos(y/x) .