-307 order and whether or not it is linear

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In summary, -307 order is a type of non-linear mathematical equation used to represent a relationship between two variables. It differs from linear and quadratic equations in that it cannot be graphed on a traditional x-y coordinate plane. The equation follows the form of y = ax^b, where b is a negative constant not equal to -1, and its graph has a curved shape. Real-life examples of -307 order relationships include population growth, radioactive decay, and the spread of infectious diseases. These equations cannot be solved using traditional algebraic methods and require advanced techniques or technology.
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karush
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Determine the order and whether or not the equation is linear.
$$x^2 \frac{{d}^{2}y}{dx^2}+x\frac{dy}{dx}+2y=\sin\left({x}\right)$$
My quess is this 2nd order, but the ans says it is linear not sure why.
 
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A DE that is written as a linear combination of its derivatives (in other words, a SUM of its derivatives) is a linear DE.
 

FAQ: -307 order and whether or not it is linear

What is -307 order and how is it different from other orders?

-307 order is a type of mathematical equation that is used to represent a relationship between two variables. It is different from other orders, such as linear or quadratic, because it is a non-linear equation that cannot be graphed on a traditional x-y coordinate plane.

Is -307 order a linear equation?

No, -307 order is not a linear equation. Linear equations have a constant rate of change and can be graphed as a straight line. -307 order, on the other hand, has a varying rate of change and cannot be graphed as a straight line.

How can you tell if an equation is a -307 order?

-307 order equations follow the general form of y = ax^b, where a and b are constants. The value of b must be negative and not equal to -1 in order for the equation to be a -307 order. Additionally, the graph of a -307 order equation will have a curved shape rather than a straight line.

What are some real-life examples of -307 order relationships?

Some real-life examples of -307 order relationships include population growth, radioactive decay, and the spread of infectious diseases. These relationships cannot be accurately represented by linear equations and require the use of a -307 order equation to model their behavior.

How can -307 order equations be solved?

-307 order equations cannot be solved using traditional algebraic methods. Instead, they require the use of advanced mathematical techniques, such as calculus, to find the values of the constants a and b. Alternatively, these equations can also be solved using technology, such as graphing calculators or computer software.

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