Gen the geometric interpretation to the equation y1 xy

Question

Question 1- Define and given an example in each of the following:

i. Differential Equation

ii. Ordinary Differential Equation

iii. Partial differential Equation

iv. Order of a Differential Equation

v. Degree of a Differential Equation

vi. Integral of a Differential Equation

vii. Linear Differential Equation of the n-th order.

Question 2-

a. What is the difference between homogenous function and homogeneous differential equation?

b. Hence which of the following are homogenous and state their corresponding degrees.

i. xy + y2

ii. x² + y²/xy

iii. x² + xye^x/y

c. Given the geometric interpretation to the equation y⁽¹⁾ + x/y = 0.

d. What is the essential difference between initial value problem and boundary value problem?