Linear differential equation

equation 4 – Linear differential
A first-order linear differential equation is an equation of the form

where and are functions of An equation that is written in this form is said to be in standard form.
To solve a linear differential equation, write it in standard form to identify the
functions and Then integrate and form the expression

which is called an integrating factor. The general solution of the equation is

Example 1: Find the general solution of
Solution
For this equation,

This implies that the general solution is






Example 2: Find the general solution of Assume
Solution; Begin by writing the equation in standard form

In this form, you can see that



This implies that the general solution is




equation 4 – Linear differential
A first-order linear differential equation is an equation of the form

where and are functions of An equation that is written in this form is said to be in standard form.
To solve a linear differential equation, write it in standard form to identify the
functions and Then integrate and form the expression

which is called an integrating factor. The general solution of the equation is

Example 1: Find the general solution of
Solution
For this equation,

This implies that the general solution is






Example 2: Find the general solution of Assume
Solution; Begin by writing the equation in standard form

In this form, you can see that



This implies that the general solution is





H.W








H.W