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263_pdfsam_math 54 differential equation solutions odd

263_pdfsam_math 54 differential equation solutions odd -...

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CHAPTER 5: Introduction to Systems and Phase Plane Analysis EXERCISES 5.2: Elimination Method for Systems, page 250 1. Subtracting the second equation in the system from the first one, we eliminate y and obtain x + y = 2 y, y = x 2 y x = x. This equation is separable (also, it is linear). Separation yields dx x = dt ln | x | = t + C x ( t ) = c 2 e t . Substituting this solution into the second equation, we obtain an equation for y : y + 2 y = x = c 2 e t . This equation is a first order linear equation. Solving we obtain
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