What is the class of this equation?

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In summary, "class" in the context of equations refers to the broad category or type of equation based on its properties and characteristics. An equation's class is determined by its degree, number of variables, and other factors such as symmetry and special terms. The most common classes of equations are linear, quadratic, cubic, exponential, polynomial, logarithmic, and trigonometric. Knowing the class of an equation is important for choosing the appropriate method for solving it and understanding its behavior. An equation can belong to multiple classes if it exhibits properties of each class.
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theqavor
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Hi all,

Please tell me the class of this equation, and if possible how to solve this kind of equations:

[itex]\Delta[/itex]u([itex]\vec{r}[/itex])=F(u([itex]\vec{r}[/itex]),[itex]\vec{r}[/itex])


Thanks in advance.
 
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  • #2
3D 2nd order non-linear - no 1st order term.
IIRC: There are no general approaches for solving this type of equation.
The trouble is that the RHS function can be ANYTHING.
 

Related to What is the class of this equation?

1. What is the meaning of "class" in the context of equations?

"Class" refers to the broad category or type of equation based on its properties and characteristics. It helps to classify equations and understand their behavior.

2. How is an equation's class determined?

An equation's class is determined by its degree, or the highest exponent of the variable, and the number of variables present. Other factors such as symmetry and the presence of special terms may also affect the class.

3. What are the different classes of equations?

The most common classes of equations are linear, quadratic, cubic, and exponential. Other classes include polynomial, logarithmic, and trigonometric equations.

4. Why is it important to know the class of an equation?

Knowing the class of an equation can help determine the appropriate methods for solving it, as different classes may require different approaches. It also provides insight into the behavior and characteristics of the equation.

5. Can an equation belong to multiple classes?

Yes, an equation can belong to multiple classes if it exhibits properties of each class. For example, a quadratic equation with a coefficient of 0 for the squared term can also be classified as a linear equation.

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