The equation above then becomes which is linear in w (since n ≠ 1). Example 1: Solve the

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y′ +p(x)y = q(x)yn y ′ + p ( x) y = q ( x) y n. where p(x) p ( x) and q(x) q ( x) are continuous functions on the interval we’re working on and n n is a real number. Differential equations in this form are called Bernoulli Equations. First

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Example: Bernoulli's Equation Assume frictionless flow in a long, horizontal, conical pipe. The diameter is 2.0 ft at one end and 4.0 ft at the other. The pressure head at the smaller end is 16 ft of water. If water flows through this

This corresponds to higher pressure and lower pressure respectively in agreement with

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The most common example of Bernoulli’s principle is that of a fluid flowing