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State the order of the following ordinary differential equations and classify them as linear or non-linear....
find the general solution of the differential equation by using the system of linear equation. please need to be solve by differential equation expert. d^2x/dt^2+x+4dy/dt-4y=4e^t , dx/dt-x+dy/dt+9y=0 Its answer will look lile that: x(t)= c1 e^-2t (2sin(t)+cos(t))+ c2 e^-2t (4e^t-3sin(t)-4cos(t))+ 20 c3 e^-2t(e^t-sin(t)-cos(t))+2 e^t, y(t)= c1 e^-2t sin(t)+ c2 e^-2t(e^t-2sin(t)-cos(t))+ c3 e^-2t(5e^t-12sin(t)-4cos(t))
Consider a second order linear time invariant system represented by the following ordinary differential equation: 4. dx(t) dt dt dt Y (s) X(s) a. Find the transfer function H(s) of the system. (5 Points)
Question 2 (1 point) Saved Classify the differential equation by order and linearity. dy co3y sin (2t COS Nonlinear, second order differential equation Linear, first order differential equation Nonlinear, first order differential equation Linear, second order differential equation
i. 1. Answer each of the following For each of the following differential equations, state the order of the equation and state whether it is linear or nonlinear. If the differential equation is linear, state whether it is homogeneous or nonhomogeneous dy + + xy = sin x dx 2 a. dx2 b. x6y(5) – x2y'" – (cos x )y – ex = 0 ii. Find the value(s) of m so that the function y = xº, x 0 is...
Problem 3. Consider the following second-order linear differential equation with the given initial conditions: I day = 6 x 10-6(x – 100) dx2 Initial Conditions at x = 0: y = 0 and dy dx = 0 Determine y at x =100, with a step size of 50 using: a) Euler's method, b) Heun's method with one correction.
1. Classify each ordinary differential equation as to order (1st, 2nd, etc) and type (linear/nonlinear). a) y' + 2y + 3y = 0 b) y" + 2yy + 3y = 0 c) y" + 2y' + 3xy - 4e" y sin 3
1. (12 points) Classify the following equations as lincar or nonlinear, and state their order. Linear or nonlincar? Order Equation + tdk + t'y = cost they + t dope + t'y = cosy. dy 2y-2
23 (1) ay Determine whether the given first-order differential equation is linear in the indicated dependent variable by matching it with the differential equation given in (7) in Section 1.1, - + 2(x) = g(x). dx (7 - 1) dx + x dy = 0; in y; in x The differential equation is ---Select--- in y and ---Select--in x.
3) Start with the non-linear force equations and rewrite this as three(3) first-order Ordinary Differential Equations (ODE) or (u, d, w
Solve 1st order non-linear differential equation by Bernoulli's equation x2 dy/dx + y2 = xy Kindly simplify every step, thanks!