Expressing a differential equation into a different format

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Thread starter Shovon00000
Start date Nov 5, 2022
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Differential Differential equation Format

In summary, differential equations can be expressed in various forms such as explicit, implicit, and parametric. To convert an explicit equation into an implicit form, one can move terms to either side of the equation. These equations can be expressed in more than one form, with the choice depending on the problem at hand and given information. Different forms can provide insight, make the problem easier to solve, and allow for different solution methods, making it important to know how to convert between forms.

Nov 5, 2022

Shovon00000

How do we express this differential equation (dy/dx)= (y/x) + tan(y/x) into this form( Mdx + Ndy=0) where M,N are functions of (x,y) ?

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Nov 5, 2022

anuttarasammyak

Gold Member

[tex]\frac{dy}{dx}=\frac{y}{x}+\tan\frac{y}{x}=-\frac{M}{N}[/tex]
why do not you make
[tex]M=\frac{y}{x}+\tan \frac{y}{x},N=-1[/tex]

Last edited: Nov 5, 2022

1. What is the purpose of expressing a differential equation into a different format?

The purpose of expressing a differential equation into a different format is to make it easier to solve and analyze. Different formats may provide different insights and approaches to solving the equation.

2. What are the different formats that a differential equation can be expressed in?

A differential equation can be expressed in various formats such as explicit form, implicit form, parametric form, polar form, and power series form.

3. How do you convert a differential equation into a different format?

The conversion process depends on the original format of the differential equation and the desired format. In general, it involves algebraic manipulations and substitutions to transform the equation into the new format.

4. Can expressing a differential equation into a different format change its solution?

No, expressing a differential equation into a different format does not change its solution. The solution to the original equation will remain the same, but the process of solving it may be different in the new format.

5. Is it necessary to express a differential equation into a different format?

No, it is not always necessary to express a differential equation into a different format. However, it can be helpful in certain situations, such as when trying to simplify the equation or when a particular format is better suited for a specific problem.