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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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- Find two solutions to 2y′′+ 5y′+ 2y= 0.arrow_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
- ACTIVITY 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_forward1. Convert the following difference equation into a first-order form: Yt = Yt-1 + 2yt-2(Yt-3 – 1)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_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_forward
- a.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_forwardStep 3 of 6: Determine the value of the dependent variable y at x = 0. Answer O bo O bi Ox Oyarrow_forwardSolve and find the domain in which the solution is defined. dy/dx = (y2-xy-x2)/x2 , y(-3)=-6arrow_forward
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