Home
Class 12
MATHS
The solution of the differential equatio...

The solution of the differential equation `x^2(dy)/(dx)cos(1/x)-ysin(1/x)=-1,` where `y->-1` as `x->oo` is

A

`y=sin(1/x)-cos(1/x)`

B

`y=(x+1)/(xsin(1/x))`

C

`y=cos(1/x)+sin(1/x)`

D

`y=(x+1)/(xcos(1//x))`

Text Solution

Verified by Experts

`x^(2)(dy)/(dx)cos(1/x)-ysin(1/x)=-1`
or `(dy)/(dx) -y/x^(2)tan(1/x)=-sec(1/x)1/x^(2)`(linear)
I.F. `=e^((-int(1/x)^(2)tan(1/x)dx))=sec(1/x)`
Thus, solution is y sec `1/x = -intsec^(2)(1/x)1/x^(2)dx=tan(1/x)+c`
Given `yto -1, x to infty`. Thus, `c=-1`
Hence, equation of curve is `y=sin(1/x)-cos(1/x)`
Promotional Banner

Similar Questions

Explore conceptually related problems

The solution of the differential equation (x+2y^3)(dy)/(dx)=y is

Find the solution of the differential equation x(dy)/(dx)=y+x^3

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

The solution of the differential equation (dy)/(dx)=1/(x y[x^2siny^2+1]) is

The solution of the differential equation (dy)/(dx)+(1)/(sqrt(1-x^(2)))=0 is

The solution of the differential equation (x^2y^2-1)dy+2xy^3dx=0 is

The solution of the differential equation, dy/dx=(x-y)^(2) , when y(1)=1, is

Solve the differential equations. (dy)/(dx)=(e^(x)+1)y

The solution of the differential equation x(x^2+1)((dy)/(dx))=y(1-x^2)+x^3logx is