## Non–Linear Equation

**Introduction: **Non-Linear equations are equations that power of function or function derivative is not equal to one. Much nonlinear equation can be transformed into linear equation and use a linear equation technique to solve them. One such equation is called in the literature as the Bernoulli Equations. This equation is

The solution method is to transfer it to linear by the v = u1−p which transform equation into

This equation can be linearized and can be solved using the linear methods. Then after the transferred equation is solved using the reversed transformation the actual solution is

**Homogeneous Equations:**

Homogeneous function is given as:

For a can be any real positive number. For this case, the transformation of

This transformed equation into

And the solution

**Variables Separable Equations:** In fluid mechanics and many other field there are differential that referred to variables separable equation. In fact, this kind of class of equation appears all over this book. For this sort equation it can be written that

The solution of this kind of equation is