Differential Equations Formula - Detailed Explanation with Examples

Last Updated on Jul 31, 2023
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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.

Formula of Differential Equation

In this formula, p(t) and g(t) are continuous functions.

The function y(t) can be expressed as:

Here,

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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

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.

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.

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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