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# ps3[1] - x and y including an arbitrary constant Chapter 2...

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Applied Mathematics E2101y Introduction to Applied Mathematics Problem Set #3, due Tuesday, 24 February 2009 Chapter 2: Supplementary Problem Observe that the ODE dy dx = 1 y - x is nonlinear in y ( x ), not separable, not homogeneous, and not of a recognizably easy form to solve for y ( x ). However, the equation dx dy = y - x , which is obtained by taking the reciprocal of the original, is a linear ODE for x ( y ), with the functional relation inverted. Solve for an implicitly deﬁned algebraic relationship between the variables
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Unformatted text preview: x and y , including an arbitrary constant. Chapter 2: Valentine’s Day Problem Filling in steps in lecture, solve the ODE (2 x-ax √ x 2 + y 2 ) + (2 y + a-ay √ x 2 + y 2 ) dy dx = 0 and graph the set of points ( x, y ) that satisfy it using Mathematica, where a = 2, 4, and 8. Chapter 2, § 2.4: “Exact” ODEs 5 8 17 24 27 32...
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