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Systems of first order equations can sometimes be transformed into a single equation of higher order. Consider the system Sr = -2r1 + x2 (a) Solve the first order equation for 1, and substitute into the second equation, thereby obtaining a second order equation for r1. Solve this equation for x, and then determine 2. (b) Find the solution of the given system that also satisfies the initial conditions 11(0) = 2, x2(0) = 3.

Systems of first order equations can sometimes be transformed into a single equation of higher order. Consider the system Sr = -2r1 + x2 (a) Solve the first order equation for 1, and substitute into the second equation, thereby obtaining a second order equation for r1. Solve this equation for x, and then determine 2. (b) Find the solution of the given system that also satisfies the initial conditions 11(0) = 2, x2(0) = 3.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter7: Conic Sections And Quadratic Systems
Section7.4: Solving Nonlinear Systems Of Equations
Problem 61E
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Systems of first order equations can sometimes be transformed into a single equation of higher order. Consider the system a = -2x1 + x2 x = x1 – 2x2 (a) Solve the first order equation for r2 and substitute into the second equation, thereby obtaining a second order equation for r1. Solve this equation for x1 and then determine x2. (b) Find the solution of the given system that also satisfies the initial conditions T1 (0) = 2, x2(0) = 3. (c) Sketch the curve (in the r1x2-plane), for t 2 0, given parametrically by the ex- pressions for x1 and r2 obtained in part b.
Transcribed Image Text:Systems of first order equations can sometimes be transformed into a single equation of higher order. Consider the system a = -2x1 + x2 x = x1 – 2x2 (a) Solve the first order equation for r2 and substitute into the second equation, thereby obtaining a second order equation for r1. Solve this equation for x1 and then determine x2. (b) Find the solution of the given system that also satisfies the initial conditions T1 (0) = 2, x2(0) = 3. (c) Sketch the curve (in the r1x2-plane), for t 2 0, given parametrically by the ex- pressions for x1 and r2 obtained in part b.
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