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Homework 19 Solution

# Homework 19 Solution - Lecture 19 MEEN 357 Homework...

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Lecture 19 MEEN 357 Homework Solution 1 Lecture-19-Homework-Solution.doc RMB 1. Consider the following nonlinear first order ordinary differential equation ( ) 3 5 1 5 where 0 2 20 dx x tx x dt = − = (19.1) a. This particular ordinary differential equation is one studied in Math 308. It is known as a Bernoulli equation. With this hint, show that the exact solution is ( ) 10 10 50 5 2005 t x t t e = + (19.2) Solution : You can solve this problem with dsolve and that is acceptable. It is also easily solved by hand. If you check out the solution method for Bernoulli equations, you will find that it is a method that works for ordinary differential equations of the form ( ) ( ) ( ) ( ) n dx t P t x t Q t x dt + = (19.3) This equation solved by first changing variables with the substitution 1 1 n y x = (19.4) In the case of (19.1), the substitution is 2 1 y x = (19.5) Given this result, it perhaps becomes evident that (19.1) can be written 2 2 1 1 1 5 5 2 2 d x t dt x = − (19.6) or, by simple rearrangement, 2 2 1 1 10 5 d x t dt x + = (19.7)

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Lecture 19
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Homework 19 Solution - Lecture 19 MEEN 357 Homework...

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