Q2/ Use RDTM to solve the following nonlinear system: - azu + 4 ay2 a²u ay2 = u - u² v + 1/1 (02/12/4 + 0²/121), at av(x,y,t) at - with initial conditions 4x² u(x, y, 0) = ex-y v(x, y, 0) = ex+y Q3/ Find Adomian polynomial A6 for the nonlinear term F(u).

Let a nonlinear system be represented by X1 = x1 sin(x,) + x2f X2 = x, e¬*2 + f² y = 2x1x2 + x3 Assume that the values for the system nominal trajectories and input are known and given by Xin, X2n and fn. +Determine the linearized state space equation of this nonlinear system.

I tried -210e^-7t but it didn't work and idk what i did wrong...

Please show all work!

Find a particular solution of the indicated linear system that satisfies the initial conditions ×₁ (0) = 5, ×₂ (0) = - 7. 1 *-[-]~*~-~[0]~-~|||| X; X' = 4 1 4 = 1 3t 7

Please find all the equilibrium points of the autonomous system. Please show work clearly I have trouble reading jumbled numbers. Thank you.

Rahul parmar

nt) Consider the discrete-time dynamical system x+1 = 4x,(1-x₂). 3 If x₁ = ³, X₁+1 Is x₂ = an equilibrium for this system? X₁ 4 Write the updating function rule as f(x) = 4x(1-x). Compute the derivative: f'(x) = Evaluate the derivative at the equilibrium: Is the equilibruim stable, unstable or neither?

Find a particular solution of the indicated linear system that satisfies the initial conditions x₁ (0)=1, x₂ (0) = 4, and x3 (0) = 6. x' = - 22-26-2 20 24 - 20 - 20 2 x; x₁ = e 2 -2t 6 -5 5 1 x₂ = ²t - 1 1 The particular solution is x₁ (t) = x₂(t)=, and x3 (t) = . 1 - 1 0

Find the general solution of the linear system. Then use the initial conditions to find the particular solution that satisfies them. Use a computer system or graphing calculator to construct a direction field and typical solution curves for the system. x' = 6x + y; y' = - 4x + y; x(0) = 1 y(0) = 0 D. x(t) = C₁e²t+C₂e5t 2t Now find y(t) so that y(t) and the solution for x(t) found in the previous step are a general solution to the system of differential equations. 2t y(t) = -4C₁e²t - ₂5t Find the particular solution. The particular solution is x(t) = C₁ and y(t) =