Differential Equations MTH 242 Lecture # 05 Dr. Manshoor Ahmed.

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Presentation transcript:

Differential Equations MTH 242 Lecture # 05 Dr. Manshoor Ahmed

Summary (Recall) Total differential. Exact differential equation. Solution Method for Exact differential equation. Differential equations which are not exact. Integrating factor.

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Bernoulli’s Equation Sometimes it is possible to convert non-linear equation into a linear equation by change of the dependent variable Definition An equation of the form is called a Bernoulli’s differential equation, where n is any real number. For n = 0 equation (1) becomes linear and for n = 1 equation (1) becomes separable & linear in y. Now for y eq (1) can be writen as ……………….. (2) ………………. (1) If we let,, then..…………….. (3)

With the help of eq. (3) & (4). Eq. (2) can be simplified to the linear eq Solving (5) for v and using leads to the solution of eq (1) …………………(4) ………………..(5),,,,

Summary Linear differential equation. Solution method. Bernoulli’s differential equation. Solution of Bernoulli’s equation.