Another important classification of differential equations is according to whether they are linear or non linear. A differential equation is said to be linear if the unknown function and all of its derivatives occurring in the equation, occur in the first degree.
The equations (1)    (2)     

are linear, while (1)

(2) are Non-linear

B. Boundary conditions

In the earlier section we have seen how to obtain to general solution of as
= f '(x) as y = f(x) + C, where the constant C is the Arbitrary constant .

If we are given a condition such as 'the value of y is 6 at x = -1' then we can find the value of this arbitrary constant C. A condition of this type is called a boundary condition . A boundary condition gives us extra information, which we can substitute in the general solution to find the value of 'C'. The solution which includes the value of 'C' is called a particular solution of the differential equation.