Worksheet 2 Solutions - MA 2930, Feb 2, 2011 Worksheet 2...

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Unformatted text preview: MA 2930, Feb 2, 2011 Worksheet 2 Solutions 1. For each of the following differential equations identify (a) its order, (b) whether its linear or non-linear, and (c) among the methods youve learned so far which you can use to solve it if any: (1) y = y 2 (2) y = y + t 2 (3) y 00 = y + t (4) y 2 = y cos t (5) sin t y = y 2 cos t Recall that the order of a differential equation is the order of the highest- order derivative of the dependent variable present in it. Also recall that the equation is linear if it is linear in the dependent variable and all its derivatives; otherwise it is called non-linear . So far we have seen two methods of solution: (a) Use of an integration factor if the equation is first-order linear (b) Separation of variables if the equation is first order and can be put in the form M ( x ) dx = N ( y ) dy Now it is clear that the eq. (1) is first-order, but non-linear and in fact separable ( y- 2 dy = dt ) (2) is first-order linear and can be solved using the integrating factor...
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Worksheet 2 Solutions - MA 2930, Feb 2, 2011 Worksheet 2...

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