Uncovering the Bernoulli Equation: Solving y'+P(x)y=Q(x)y^n

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In summary, Bernoulli in disguise is a concept in physics that refers to Bernoulli's principle, which explains the relationship between pressure and velocity in a fluid. Bernoulli in disguise works by stating that as the velocity of a fluid increases, its pressure decreases. This principle is important because it helps us understand and predict fluid behavior and has practical applications in areas such as aerodynamics and plumbing. An example of Bernoulli's principle in everyday life is the flow of air over a curved surface. Bernoulli in disguise is essentially the same as Bernoulli's principle, with the added emphasis on its hidden or unexpected nature.
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physicsnewb7
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Homework Statement


I think this is a bernoulli equation in disguise
(y^7-6x)y'+y=0

Homework Equations


I'm having trouble putting it in the form of y'+P(x)y=Q(x)y^n


The Attempt at a Solution


I've tried to divide out (y^7-6x) as well as some other alebraic manipulation but i keep getting stuck. Any advice?
 
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anyone?
 
  • #3
physicsnewb7 said:
anyone?

Try writing it in terms of [itex]x = x(y)[/itex] and using:

[tex]
y' = \frac{1}{x'}
[/tex]
 

1. What is Bernoulli in disguise?

Bernoulli in disguise is a concept in physics that refers to the principle of fluid dynamics known as Bernoulli's principle, which describes the relationship between pressure and velocity in a fluid.

2. How does Bernoulli in disguise work?

Bernoulli's principle states that as the velocity of a fluid increases, its pressure decreases. This means that when a fluid is moving quickly, it exerts less pressure on its surroundings than when it is moving slowly. This principle can be applied to various phenomena, such as the lift of an airplane wing or the flow of water through a pipe.

3. Why is Bernoulli in disguise important?

Bernoulli's principle is important because it helps us understand and predict the behavior of fluids in various situations. It is also the basis for many practical applications, such as the design of airplane wings, car aerodynamics, and plumbing systems.

4. Can you give an example of Bernoulli in disguise in everyday life?

One example of Bernoulli's principle in everyday life is the flow of air over a curved surface, such as a car's roof. As the air flows over the curved surface, its velocity increases and its pressure decreases, creating a downward force that helps keep the car stable and on the ground.

5. How is Bernoulli in disguise different from Bernoulli's principle?

Bernoulli in disguise is simply another way of referring to Bernoulli's principle. The term "in disguise" is often used to emphasize the unexpected or hidden nature of the principle and how it can be applied in various situations.

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