wksht02 - MATH 152 L1& L2 Applied Linear Algebra and...

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Unformatted text preview: MATH 152 L1 & L2 Applied Linear Algebra and Differential Equations Spring 2004-05 ¥ Week 02 Worksheet (February 7, 2005) : First-order differential equations Q1. (Change of variables) Consider the first-order differential equation 1 + x y- sin y ¶ dy dx = 0 , which is neither linear nor separable. The purpose of this problem is to show you a trick. (a) Instead of thinking of the variable y as a function of x , suppose we think of the variable x as a function of y . The derivative of x with respect to y is dx dy , the reciprocal of dy dx . Rewrite the given equation so that it is an equation for dx dy . (b) Is your rewritten equation linear, separable or both? (c) Solve your differential equation for x as a function of y . This gives you an implicit function for y in terms of x . Q2. (Homogeneous equation) In the previous problem, we showed how one sometimes converts nonlinear differential equations into linear differential equations. This problem shows you another trick to convert a certain type of differential equation into a separable equation. Let us consider the equationa certain type of differential equation into a separable equation....
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This note was uploaded on 09/30/2010 for the course MATH MATH152 taught by Professor Kcc during the Spring '10 term at HKUST.

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wksht02 - MATH 152 L1& L2 Applied Linear Algebra and...

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