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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- Determine if y = ex is a solution to y′′′- 12y′′ + 48y′- 64y=0arrow_forwardA Moving to another question will save this response. Question 12 Find the solution of x²y" + xy-4y=0 where y(1) = 0 and y (1) = 4arrow_forwardDetermine which one of the following equations are linear equation. If nonlinear identify the nonlinear terms. 2V – yx+ zx =cos 1 (i) 1 CoS (ii) x +*+ elnz +w = 4 yarrow_forward
- Find 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_forwardQuestion 10: The solution of the following linear equation xy' + 2y = x² – x +1 is: a. y: b. y =: 3 3/4 c.y ==-arrow_forwardGeneral Solutions and Phase Portraits. In each of Problems 1 through 6, find the general solution of the given system of equations. Also draw a direction field and a phase portrait. Describe how the solutions behave as t → ∞. 3 1. x' = Xarrow_forward
- Solve the following equation: y''+4y'+7y=0arrow_forward1. Convert the following difference equation into a first-order form: Yt = Yt-1 + 2yt-2(Yt-3 – 1)arrow_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_forward
- 4. Find the first three nonzero terms in each of two linearly independent solutions of the equation. (1+x²)y" + xy = 0arrow_forwardSolve for particular solution. (2x-6y+4)dx + (x-2y-3)dy = 0 ; when x = 1, y = 1arrow_forwarda.Draw a direction field and sketch a few trajectories. b.Describe how the solutions behave as t → ∞ . c.Find the general solution of the system of equations. 2.x′=(4−28−4)xarrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,