3. We consider differential equations of the form (a) Suppose we have found (by some means)...
Consider the following non-homogeneous system of differential
equations.
a. Write the system in matrix form.
b. Find the homogeneous solution.
c. Find the particular solution.
d. Write down the general solution.
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Question 3 Consider the following linear system of differential equations dx: = 2x-3y dt dy dt (a) Write this system of differential equations in matrix form (b) Find the general solution of the system (c) Solve the initial value problem given (0) 3 and y(0)-4 (d) Verify the calculations with MATLAB
Question 3 Consider the following linear system of differential equations dx: = 2x-3y dt dy dt (a) Write this system of differential equations in matrix form (b) Find the...
Consider the following linear system of differential equations: dx/dt = 2x-3y dy/dt = -x +4y (a) Write this system of differential equations in matrix form (b) Find the general solution of the system (c) Solve the initial value problem given x(0) = 3 and y(0) = 4 (d) Verify the calculations with MATLAB
Previous Problem Problem List Next Problem (10 points) This problem is related to Problems 9.33-9.38 in the text. We have solved differential equations using the method of undetermined coefficients (Chapter 7) and Laplace transforms (Chapter 8). We can use Fourier series to find the particular solution of an arbitrary order differential equation - as long as the driving function is periodic and can be represented by a Fourier series In the problem description and answers, all numerical angles(phases) should be...
Question 2 Consider the differential equation We saw in class that one solution is the Bessel function (a) Suppose we have a solution to this ODE in the form y-Σχ0CnXntr where cn 0. By considering the first term of this series show that r must satisfy r2-4-0 (and hence that r = 2 or r =-2) (b) Show that any solution of the form y-ca:0G,2n-2 must satisfy C0 (c) From the theory about singular solutions we know that a linearly...
Consider the differential equation: -9ty" – 6t(t – 3)y' + 6(t – 3)y=0, t> 0. a. Given that yı(t) = 3t is a solution, apply the reduction of order method to find another solution y2 for which yı and y2 form a fundamental solution set. i. Starting with yi, solve for w in yıw' + (2y + p(t)yı)w = 0 so that w(1) = -3. w(t) = ii. Now solve for u where u = w so that u(1) =...
Differential Equations with MATLAB/Plotting first order
differential equations in Matlab/ Differential Equations MATLAB/IVP
Matlab/IVP
I'd really appreciate if I can get some help plotting these 3
first order differential equations as well as their comments.
PLEASE! ANYTHING HELPS, I am very stuck :(
EZplot and ODE 45 were mentioned in class and the instructions
in class were not clear at all.
Given the first order differential equation with initial condition. dy/dt = y t, y(0)=-1 Complete problems 1-3 in one...
Problem 3: Insights into Differential Equations a. Consider the differential equation 습 +4 = f(t), where f(t) = e-u, 12 0. Please write the forms of the natural and forced solution for this differential equation. You DO NOT need to solve. (7 points) b. Again consider the differential equation f(t), where f(t) is an input and y(t) is the output (response) of interest. Please write the differential equation in state-space form. (10 points) c. The classical method for solving differential...
DO HAND CALCULATIONS. SHOW ALL STEPS
1. Slope Fields For the given differential equations sketch the slope fields and some of the isoclines. Then sketch some of the solution curves and verify your answer by solving the differential equation. a) dy-2 dx y
1. Slope Fields For the given differential equations sketch the slope fields and some of the isoclines. Then sketch some of the solution curves and verify your answer by solving the differential equation. a) dy-2 dx y
The solution of a certain differential equation is of the form y(t)=a exp(3t) + bexp(8t), where a and b are constants.The solution has initial coniditons y(0) and y’(0)=1.Find the solution by using the initial conditions to get linear equations fro a and by(t)=?