Determine whether the given equation is seperable linear nei

Determine whether the given equation is seperable, linear, neither or both.

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

Solution

y and dy/dx has power equal to 1 hence the equation is linear

Right hand side term has no y term so the equation cannot be separable.

Hence the equation is linear but not separable.