determine the order and if the DE is Linear or non-Linear.
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determine the order and if the DE is Linear or non-Linear. 5. J2 t, sin(t +...
Question 1 5 pts What is the order of the DE? Is the DE linear or nonlinear? 3 54' - (tan x)y= Vx+ +1 (7) 5.22 3rd order; nonlinear 2nd order; nonlinear 2nd order; linear 3rd order; linear LUCSLIUI 5 pts Is the function y=2e-32 - 4e5x a solution to the DE? Y' - 2y - 15y = 0 O No O Yes Question 3 5 pts Solve the separable DE. dy 3.cy + 2y - 15x - 10 dac...
1. Identify each of the following equations as linear or nonlinear and also determine their order dy (a) y = t 3 3 (b) ( dy + (c) sin t (d) (1y) sin t ( cos2 t 1 y sin(t)= 0 (e) Int +3etdy dt (f) 2y'-y2 =e (g) y"(t2 1)y+cos(t (h) y"sin(ty)y(t21)y 0 = 0
1. Identify each of the following equations as linear or nonlinear and also determine their order dy (a) y = t 3 3 (b)...
Consider the folowing 2nd-order linear non-homogeneous DE, 1'- 12y' + 36y = 18c6x The complimentary solution of the equation is Yo (x) = where ci and C2 are arbitrary constants. A particular solution of the equation is yp (x) = 1 The general solution of the non-homogeneus equation is y(x) = symbolic formatting help Consider the following 2nd-order linear non-homogeneous DE, y" – 20y' + 100y = (2x + 14) 207 The complimentary solution of the equation is y. (x)...
Which of the following is of the form of a non-homogeneous second-order linear DE? OR(Cy" + P(Zy' +Q(2y = f(2) O P(1)y' +Q(I)y = 0 OR(Cy" + P(2)y' +Q(I)y=0 O none of the other options O P(x)y' +Q(z)y = f(x)
5) Consider the second order linear non-homogeneous differential equation tay" - 2y = 3t2 - 1,t> 0. a) Verify that y(t) = t- and y(t) = t-1 satisfy the associated homogeneous equation tay" - 2y = 0. (5 points) b) Find a particular solution to the non-homogeneous differential equation. (10 points) c) Find the general solution to the non-homogeneous differential equation. (5 points)
Use MATLAB’s ode45 command to solve the following non linear 2nd order ODE: y'' = −y' + sin(ty) where the derivatives are with respect to time. The initial conditions are y(0) = 1 and y ' (0) = 0. Include your MATLAB code and correctly labelled plot (for 0 ≤ t ≤ 30). Describe the behaviour of the solution. Under certain conditions the following system of ODEs models fluid turbulence over time: dx / dt = σ(y − x) dy...
Classify each ode as linear or non linear, autonomous or not. If an ode is linear classify it as homogenous or non homogeneous. 1) y' = y 2) y = e-t sin y 3) y = y' +t > 4) = 1 5) (Int)y' = yey
8. Determine the appropriate form of the particular solution for the following non-homogeneous linear differential equation with constant coefficients. (8 Puan y(4) +9y" = 5+ &'(x-3) + 4sin (3x). none of these O Ar? + Bx cos(3x) + Cx sin(3x) + De' + Exet Ar + B + C sin(3x) + D cos(3x) + Exe" A + Bre-3x + Crer + De + Exet O Ar? + Bxe- + Crex + Det + Exe! A + B sin(3x) + Cxsin(3x)...
The system of non-linear differential equations sin cosy sin x + cos( y), has an equilibrium point at (0,T) (a) Calculate the Jacobian matrix of this system of equations and evaluate this matrix at the given equilibrium point. (b) Use your answer to part (a) to classify this equilibrium point.
The system of non-linear differential equations sin cosy sin x + cos( y), has an equilibrium point at (0,T) (a) Calculate the Jacobian matrix of this system of equations and...
8. Determine the appropriate form of the particular solution for the following non-homogeneous linear differential equation with constant coefficients. * (8 Puan) y (4) +9y" = 5+ (x-3) + 4sin(3x). A + B sin(3x) + Cx sin(3r) + Det + Exer A + Bxe-3x + Cxex + De' + Exet Ax? + Bxe-3x + Cxe3x + Det + Exel none of these Ax? + Bx cos(3x) + Cx sin(3x) + Del + Exe" Ax+ B + C sin(3x) + D...