Exact differential equation examples and solutions

1. What is exact differential equation with example?
2. How do you find the exact solution of a differential equation?
3. How many types of differential equation and explain with examples?
4. What is an exact solution?

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.

How do you find the exact solution of a differential equation?

Once a differential equation M dx + N dy = 0 is determined to be exact, the only task remaining is to find the function f ( x, y) such that f _x = M and f _y = N.

How many types of differential equation and explain with examples?

While differential equations have three basic types—ordinary (ODEs), partial (PDEs), or differential-algebraic (DAEs), they can be further described by attributes such as order, linearity, and degree.

What is an exact solution?

As used in physics, the term "exact" generally refers to a solution that captures the entire physics and mathematics of a problem as opposed to one that is approximate, perturbative, etc. Exact solutions therefore need not be closed-form.