For the below ordinary differential equation state the order

For the below ordinary differential equation, state the order and determine if the equation is linear or nonlinear. Then find the general solution of the ordinary differential equation. Verify your solution. (x^2 - y^2)dx + (y^2 - 2xy)dy = 0

Solution

This is a first order non-linear differential equation.

Rewrite this equation as

(x² dx+y² dy)-(y² dx+2xydy) =0

and observe that both terms inside the brackets are exact.

Thus we obtain the solution

x³ +y³ -3 xy² =C