Differential equations are mathematical equations that involve one or more functions and their corresponding derivatives. These equations play a crucial role in various fields, including physics, engineering, and economics. If the equation includes partial derivatives, it is referred to as a partial differential equation. The order of a differential equation is determined by the highest order derivative present in the equation.
Differential Equations Formula - Detailed Explanation with Examples
Last Updated on Jul 31, 2023
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Formula of Differential Equation
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In this formula, p(t) and g(t) are continuous functions.
The function y(t) can be expressed as:
Here,
Example of a Differential Equation
Example:
= 9.1 – 0.18v, v(0) = 46 , find the solution to this differential equation.
Solution:
Using the integrating factor, the differential equation becomes:
Integrating on both sides, we get:
Given, v(0) = 46
⇒ v(0) = 46 + ce -0.18(0)
⇒ 46 = 46 + c
⇒ c = 0
Hence, v(t) = 46
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Frequently Asked Questions
What is a Differential Equation?
A differential equation is an equation with one or more functions and their derivatives. It is also called as Partial differential equations if they have partial derivatives.
What is the formula for a Differential Equation?
The formula for a Differential Equation is dy/dt + p(t)y = g(t), where p(t) & g(t) are the functions which are continuous.
How to solve a Differential Equation?
To solve a differential equation, you need to find an Integrating factor, form a differential equation using this factor and then integrate on both sides.
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