The solution of differential equation x^...

The solution of differential equation `x^(2)(x dy + y dx) = (xy - 1)^(2) dx` is (where c is an arbitrary constant)

A

`xy-1=cx`

B

`xy-1=cx^(2)`

C

`(1)/(xy-1)=(1)/(x)+c`

D

`(1)/((xy-1)^(3))=(1)/(x^(3))+c`

Verified by Experts

The correct Answer is:

C

`x^(2)(xdy+ydy)=(xy-1)^(2)dx" "rArr" "int(d(xy))/((xy-1)^(2))=int(dx)/(x^(2))" "rArr" "(-1)/(xy-1)=(-1)/(x)+c`

Similar Questions

Explore conceptually related problems

What is the general solution of the differential equation x dy - y dx = y^(2)dx ? Where C is an arbitrary constant

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

The solution of the differential equation dy - (ydx)/(2x) = sqrt(x) ydy is (where , c is an arbitrary constant)

The solution of the differential equation xdy-ydx+3x^(2)y^(2)e^(x^(3))dx=0 is (where, c is an arbitrary constant)

what is the solution of the differential equation (dx)/(dy) +x/y -y^(2) =0 ? where c is an arbitraty constant .

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

Solution of the differential equation (1+x^(2)) dy + 2xy dx = cot x dx is