Here you will learn general form of first order first degree differential equations and methods of solving first order first degree.
Let’s begin –
General Form of First Order First Degree Differential Equations
A differential equation of first order and first degree involves the independent variable x, dependent variable y, and \(dy\over dx\). So, it can be put in any one of the following forms
\(dy\over dx\) = f(x, y)
or, \(dy\over dx\) = \(\phi (x, y)\over \psi (x, y)\)
or, In general f(x, y, \(dy\over dx\)) = 0, where f(x, y) and g(x, y) are obviously the functions of x and y.
Solution of First order and First Degree Differential Equations
As discussed earlier a first order and first degree differential equation can be written as
f(x, y)dx + g(x, y)dy = 0 or \(dy\over dx\) = \(f(x, y)\over g(x, y)\) or, \(dy\over dx\) = \(\phi(x, y)\)
where f(x, y) and g(x, y) are obviously the functions of x and y.
It is not always possible to solve this type of equations. The solution of this type of differential equations is possible only when it falls under the category of some standard forms. In the following section we will discuss some of the standard forms and methods of obtaining their solutions.
Methods of Solving a First order First Degree
These are the several techniques of obtaining solutions of following types of differential equations.
(i) Differential Equations of the form \(dy\over dx\) = f(x) or \(dy\over dx\) = f(y)
(ii) Differential Equations in variable seperable form
(iii) Differential Equations reducible to variable separable form
(iv) Homogeneous Differential Equation