Which of the following equations are separable xyy2x2 dydx1x

Which of the following equations are separable xy\'-y=2x^2; dy/dx=1+x^2/y-1; y\'-x^2y=0. Do not solve.

Solution

Here first and third are linear differential equations of form dy/dx +Py=Q where P and Q are functions of x.

So it these equations are not separable.

Further the second equation dy/dx = (1+x^2)/(y-1)

on cross multiply, can be written as :

(y-1) dy = (1+x^2) dx

that is clearly separable now.

So correct answer is option (b).