MATH 2270 Lecture Notes - Lecture 4: Orthogonal Trajectory, Bernoulli'S Principle, Integrating Factor
21 Dec 2013
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There are several other special equations that may be solved by transforming to another variable to solve in. (think: integration by substitution, but with des. ) For all of the following examples, we will use y as the dependent variable and x as the independent variable. Some equations can be solved by making a substitution where we let the dependent variable be equal to some function of the independent variable multiplied by the independent variable. This can be helpful in transforming an ode into a separable equation that can easily be solved. Solve dy dx x3 + 2x2 + y x (2. 106) This is a non-separable rst-order ode, and in fact it can be solved by nding an integrating factor. (as we saw on assignment 1!) Let"s solve it another way, by rst letting y(x) = v(x)x. Then, using the product rule, into the equation, we obtain dy dx dv dx. + v = x3 + 2x2 + vx x.
