5. Methods of Solving First Order, First Degree Differential Equations and Differential equations with variables separable

Methods of Solving First Order, First Degree Differential Equations

There are three methods to solve the first-order, first-degree differential equations. They are:

1. Differential equations with variables separable
2. Homogeneous differential equations
3. Linear differential equations

Differential equations with variables separable:

A first order-first degree differential equation is of the form

If F (x, y) can be expressed as a product g (x) h(y), where, g(x) is a function of x and h(y) is a function of y, then the differential equation (1) is said to be of variable separable type. The differential equation (1) then has the form

If h (y) ¹0, separating the variables, (2) can be rewritten as

Integrating both sides of (3), we get

Thus, (4) provides the solutions of given differential equation in the form

H(y) = G(x) + C

Example: Find the general solution of the differential equation 

which is the general solution of equation (1).