Bernoulli's equation differential equations example

This calculus video tutorial provides a basic introduction into solving bernoulli's equation as it relates to differential equations. You need to write the

Bernoulli Equation

In this video tutorial provides the basic introduction of solving a differential equation in the form of Bernoulli's equation of first order first degree. Wr
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Bernoulli differential equations

Bernoulli equation: dy dx + y x = y3 with P(x) = 1 x,Q(x) = 1,n = 3 DIVIDE by yn i.e. y3: 1 y3 dy dx + 1 x y βˆ’2 = 1 SET z = y1 βˆ’n i.e. z = yβˆ’2: dz dx = βˆ’2y 3 dy dx i.e. βˆ’1 2 dz dx = 1 y3 dy dx ∴ βˆ’ 1 2 dz
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Solution of Bernoullis Equations

Example 1: Solve. dy dx + x 5 y = x 5 y 7. It is a Bernoulli equation with P (x)=x 5, Q (x)=x 5, and n=7, let's try the substitution: u = y 1βˆ’n. u = y -6. In terms of y that is: y = u (βˆ’1 6) Differentiate y with respect to x: dy dx = βˆ’1 6 u (βˆ’7 6) du dx.

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Bernoulli Differential Equations Examples 1

The most common example of Bernoulli’s principle is that of a fluid flowing through a horizontal pipe, which narrows in the middle and then opens up again. This is easy to

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MATHEMATICA TUTORIAL, Part 1.2: Bernoulli Equations

dy dx + 2xy = x2y2 To solve the differential equation, let v = y1 - n where n is the exponent of y2. v = y - 1 Solve the equation for y. y = v - 1 Take the derivative of y with respect to x. yβ€² = v - 1 Take

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