# 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 β2 = 1 SET z = y1 βn i.e. z = yβ2: dz dx = β2y 3 dy dx i.e. β1 2 dz dx = 1 y3 dy dx β΄ β 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 1βn. u = y -6. In terms of y that is: y = u (β1 6) Differentiate y with respect to x: dy dx = β1 6 u (β7 6) du dx.

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## Bernoulli Differential Equations Examples 1

The most common example of Bernoulliβ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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