Ch 06/Bernoulli Equations/H.K. Dass 3.10

Bernoulli Equations

A Bernoulli equation has the form dy/dx + Py = Qy^n. Divide by y^n, substitute z = y^(1-n) to convert it into a linear equation.

IThe Bernoulli Reduction

The form: where .

Method:

1. Divide by

2. Let

3. Equation becomes linear:

4. Solve using I.F. method

5. Recover from .

Example 1easy

Solve .

Show step-by-step solution+

Rewrite

. Bernoulli with .

Divide by y^2, put z = 1/y

. I.F. .

Answer

Example 2medium

Solve .

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Bernoulli

. Divide by , put .

Linear equation

. I.F. .

Answer

Example 3medium

Solve .

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Multiply by sec y

Substitute z = sec y

. I.F. .

Answer

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