First-Order Linear Differential Equations

Introduction to First-Order Linear Differential Equations

A first-order linear differential equation is an equation that is linear in the dependent variable and its derivative. It can be represented in the form y' + p(x)y = q(x), where y is the dependent variable, x is the independent variable, y' is the derivative of y with respect to x, and p(x) and q(x) are known functions of x. The solution to the equation is given by y = mx +c, where m is the slope of the line and c is the y-intercept.

Parameter usage:

• m= slope of the line
• x= value of the independent variable
• c= y-intercept

Output:

• y= value of the dependent variable

Data validation

No specific data validation is needed for this formula.

Summary

This calculator takes into account the slope of the line, value of the independent variable, and y-intercept to calculate the value of the dependent variable in a first-order linear differential equation.