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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 it’s linear or nonlinear, and (c) among the methods you’ve 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 nonlinear . So far we have seen two methods of solution: (a) Use of an integration factor if the equation is firstorder 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 firstorder, but nonlinear and in fact separable ( y 2 dy = dt ) (2) is firstorder linear and can be solved using the integrating factor...
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 Spring '07
 TERRELL,R
 Differential Equations, Equations, Trigraph, Constant of integration

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