The Bernoulli differential equation is (dy /dt) + a(t) y = b(t) y ". Multiplying through

Chapter 1, Problem 20

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QUESTION:

The Bernoulli differential equation is (dy /dt) + a(t) y = b(t) y ". Multiplying through by p(t) = exp , we can rewrite this equation in the form d/dt( p(t)y) = b(t) p(t) y ". Find the general solution of this equation by finding an appropriate integrating factor. Hint: Divide both sides of the equation by an appropriate function of y.

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QUESTION:

The Bernoulli differential equation is (dy /dt) + a(t) y = b(t) y ". Multiplying through by p(t) = exp , we can rewrite this equation in the form d/dt( p(t)y) = b(t) p(t) y ". Find the general solution of this equation by finding an appropriate integrating factor. Hint: Divide both sides of the equation by an appropriate function of y.

ANSWER:

Step 1 of 4

Consider the Bernoulli’s equation is,

                                                                     

Solve the equation as,

                                                                     

Since,  and

                                                                     

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