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General Solutions of Systems. In each of problems 1 through 12, find the general solution of the given system of equations. Also draw a direction field and a phase portrait. Describe the behaviour of the solutions as
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Differential Equations: An Introduction to Modern Methods and Applications
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- 1. Convert the following difference equation into a first-order form: Yt = Yt-1 + 2yt-2(Yt-3 – 1)arrow_forwardFind the solution of the following equations using method of substitutions. A. (2x-2y+1)dx + (3y-3x-2)dy = 0arrow_forwardDetermine which one of the following equations are linear equation. If nonlinear identify the nonlinear terms. (i) 2x – y + z - t = sin- 2 (ii) x ++z+w = 4 yarrow_forward
- Solve for particular solution. (2x-6y+4)dx + (x-2y-3)dy = 0 ; when x = 1, y = 1arrow_forwardACTIVITY 3 Direction: solve and analyze each of the following problem in neat and orderly manner. Do this in your indicated format. Determine the general solutions of the following non homogenous linear equations. 1. (D2 + D)y = sin x 2. (D2 - 4D+ 4)y = e* 3. (D2 - 3D + 2)y = 2x3-9x2 + 6x 4. (D2 + 4D+ 5)y 50x + 13e3x 5. (D3 - D2 + D- 1)y 4 sin x 6. (D3-D)y = x -END OF MODULE 3---arrow_forwardFind the general solution of the given system. Use a computer system or graphing calculator to construct a direction field and typical solution curves for the system. x′= 5 1 −4 1 x What is the general solution to the system? x(t)=arrow_forward
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