Find dy at x = dt - 5 if y = – 3x2 – 1 and dx = - 5. dt dy dt
Solve for y(t). dy/dt + 2x = et dx/dt-2y= 1 +t when x(0) = 1, y(0) = 2
12 dạy dy 6 +9y=4e3t; when t=0, y = 2 dt dy and dt dt2 = 0
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
slove the system eqution: d^3y(t)/dt^3 - 2 d^2y(t)/dt^2 - 5 dy(t)/dt +6 y(t) = 2 d^2u(t)/dt^2 +du(t)/dt +u(t) A) compute the transfer function Y(s)/U(s)? B)Find inverse Laplace for y(t) and x(t)? C) find the final value of the system? D)find the initial value of the system? Please solve clearly with steps.
Suppose you have to solve the following system by elimination d²x dy j? y dy 9y+672 + + 8y = 82 + 5 sint dt2 dt dc + + 3х dt dt2 dt The standard form of the system is O (2D - 8)x+ (D+ 8)y = 5 sint (D - 3)2 + (2D+D+9)y= 6t2 (D2 – 8)x+ (D+8)y= 5 sint (D-3)x +(D2 +D+9)y+ 6+2 = 0 (D2 - 8)2 + (D+ 8)y - 5 sint = 0 (D –...
sketch phase lines for: dy/dt = y(y+3)^3(y-2)^2(y-5) sketch bifurcation diagram for: dy/dt = y(y^2+ α) where α is a parameter
Solve IVP 23·-=-5x-y dt dy = 4x-y dt x(1) = 0, y(1) = 1
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)) =
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...