MATH24 Lecture 2 with correction

MATH24 Lecture 2 with correction - MATH24 Differential...

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MATH24 Differential Equations
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Definitions Arbitrary Constants and Parameters An arbitrary constant is a constant that does not have a fixed value and is eliminated from an equation to form its differential equation while a parameter, usually treated as a constant, is not to be eliminated.
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Steps in Eliminating Arbitrary Constants 1. Differentiate the equation as many times as the number of arbitrary constants. 2. Eliminate the arbitrary constants from the equation and its derivatives by a suitable method. Notes: 1. The desired differential equation is free from arbitrary constants. 2. The order of the resulting differential equation should be equal to the number of arbitrary constants.
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Examples Find the differential equations of the following by eliminating the arbitrary constants. 1. y = 3x 2 + ce −2x 2. y = C 1 sin4x + C 2 cos4x + x 3. y = (x + c)e −x 4. x + y = tan(x + c) Recall: tan −1 u = (du/dx)/(1 + u 2 ) 5. (x − a) 2 + y 2 = a 2 Families of Circles with center at (a, 0) and passing through the origin.
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MATH24 Lecture 2 with correction - MATH24 Differential...

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