Find the solution of the differential equation:

Find the differential equation which has y = c₁ e^x + c₂ e^-x as the general solution.

Prove that y²dx + (x² – xy – y²)dy = 0 is a homogenous differential equation. Also, find the degree of the equation.

Find the solution of the differential equation , y(0) = 1 approaches to zero, when x → ∞.

Find the differential equation of the family of lines through the origin.