Solve Non Homogeneous Equations: Formulas & Solutions

  • Thread starter Miike012
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In summary, a non-homogeneous equation is a type of differential equation that contains an additional term or function on one side of the equation, making it more challenging to solve compared to homogeneous equations. The main difference between homogeneous and non-homogeneous equations is the presence of this extra term. To solve a non-homogeneous equation, the general formula involves finding the solution to the corresponding homogeneous equation and combining it with a particular solution. This particular solution can be found using the method of undetermined coefficients or the method of variation of parameters. Non-homogeneous equations have various applications in science, such as modeling real-world phenomena in physics, engineering, and data analysis.
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Miike012
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Are there any formulas so solve for the particular solution of non homeg equations?
If anyone knows where I can find them on the net please let me know thanks.
 
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  • #2
Google the name of the method.
Annihilator Method
Method of Underdetermined Coefficients
Variation of Parameters
Laplace Transforms
or you could consult a book such as Dennis Zills book a First Course in Differential Equations
 

What is a non-homogeneous equation?

A non-homogeneous equation is a type of differential equation in which the dependent variable and its derivatives are not equal to zero on one side of the equation. This means that there is an additional term or function present in the equation, making it more complex to solve compared to homogeneous equations.

What is the difference between homogeneous and non-homogeneous equations?

The main difference between homogeneous and non-homogeneous equations is the presence of an additional term or function in the equation. Homogeneous equations have all terms and functions equal to zero on one side, while non-homogeneous equations do not. This extra term makes non-homogeneous equations more challenging to solve.

What is the general formula for solving non-homogeneous equations?

The general formula for solving non-homogeneous equations is to first find the solution to the corresponding homogeneous equation. This solution is then combined with the particular solution, which is a specific solution that satisfies the non-homogeneous equation. The final solution is the sum of these two parts.

How do I find the particular solution to a non-homogeneous equation?

The particular solution to a non-homogeneous equation can be found using the method of undetermined coefficients or the method of variation of parameters. These methods involve finding a solution that satisfies the non-homogeneous equation and then using it to determine the particular solution.

What are some common applications of non-homogeneous equations in science?

Non-homogeneous equations are commonly used in physics, engineering, and other scientific fields to model real-world phenomena, such as heat transfer, fluid flow, and electrical circuits. They are also used in mathematical modeling and data analysis to describe complex systems and make predictions based on data.

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