A particular solution X, of dx dt dy dt -(-11)[*]+(??)e2 2t where X-C1 - (11) oxca[(-2.Jte2+...
dx/dt = -2x-4y dy/dt = 0.5x draw the x(t) graph for the solution that starts at (x,y)=(1,1)
Consider the following system: dx/dt=y(x^2+y^2-1) dy/dt= -x(x^2 +y^2-1) Find the equilibrium solution. 13. Consider the following system dx dy (e) Find the equilibrium solutions (0 Use Maple to sketch a phase portrait (me to understand the qualitative behavior of 13. Consider the following system dx dy (e) Find the equilibrium solutions (0 Use Maple to sketch a phase portrait (me to understand the qualitative behavior of
Problem 3. Consider the following continuous differential equation dx dt = αx − 2xy dy dt = 3xy − y 3a (5 pts): Find the steady states of the system. 3b (15 pts): Linearize the model about each of the fixed points and determine the type of stability. 3b (15 pts): Draw the phase portrait for this system, including nullclines, flow trajectories, and all fixed points. Problem 2 (25 pts): Two-dimensional linear ODEs For the following linear systems, identify the...
Find dz d given: z = xeyy, x = = to, y= – 2 + 2t dz dt Your answer should only involve the variable t. Let z(x, y) = xºy where x = tº & y = +8. Calculate dz by first finding dt dx -& dt dy and using the chain rule. dt dx d = dy dt Now use the chain rule to calculate the following: dz dt
Find dy/dt using the given values. y = x - 4x for x = 3, dx/dt = 2. y = [ X dt . dx/dt = 2. Enter an exact number
(1 point) Find a particular solution to dy dy x2 + 4x + 2y =x' sin(x). dx in x > 0 ур (1 point) Find a particular solution to dy dy x2 + 4x + 2y =x' sin(x). dx in x > 0 ур
Consider the following system. dx dt dy dt 5 x + 4y 2 3 =X - 3y 4 Find the eigenvalues of the coefficient matrix Alt). (Enter your answers as a comma-separated list.) Find an eigenvector for the corresponding eigenvalues. (Enter your answers from smallest eigenvalue to largest eigenvalue.) K K₂ = Find the general solution of the given system. (x(t), y(t)) =
Find the solution to the given systems (a) X'=X X(0)= (b) dx/dt=5x+y dy/dt=-2x+3y We were unable to transcribe this imageWe were unable to transcribe this image
Question 4 A power series solution about x = 0 of the differential equation dy dx +(x+2)y = is Select the correct answer. y=00(1-2x+2x2-3x2) OnY=60(1+2x+3x2+3x... Oc. None y=a01 - 21x2+x- Od
Solve the given system of differential equations by systematic elimination. 2 dx/dt − 4x + dy dt = et dx/dt − x + dy dt = 3et