Exact differential equations pdf

1. What is exact differential equation with example?
2. What is meant by exact differential equation?
3. How do you solve exact differential equations?
4. What is the application of exact differential equation in our real life?

What is exact differential equation with example?

Exact Differential Equation Examples

Some of the examples of the exact differential equations are as follows : ( 2xy – 3x² ) dx + ( x² – 2y ) dy = 0. ( xy² + x ) dx + yx² dy = 0. Cos y dx + ( y² – x sin y ) dy = 0.

What is meant by exact differential equation?

A first-order differential equation (of one variable) is called exact, or an exact differential, if it is the result of a simple differentiation. The equation P(x, y)^dy_dx + Q(x, y) = 0,or in the equivalent alternate notation P(x, y)dy + Q(x, y)dx = 0,is exact if ^{∂P(x, y)}_∂x = ^{∂Q(x, y)}_∂y.

How do you solve exact differential equations?

Let us consider the equation P(x, y)dx + Q(x, y)dy equal to 0. Suppose that there exists a function v(x, y) such that dv = Mdx + Ndy, then the differential equation is said to be an exact differential equation solution is given by v(x, y) = c. Suppose that (1) is exact. Hence the given equation is exact.

What is the application of exact differential equation in our real life?

Ordinary differential equations applications in real life are used to calculate the movement or flow of electricity, motion of an object to and fro like a pendulum, to explain thermodynamics concepts. Also, in medical terms, they are used to check the growth of diseases in graphical representation.