3. Exercise §2.4 #9. (May use any method). Solve the diffusion equation ut = kuzz with the initial condition u(x,0) = x² by the following special method. First show that uz satisfies the diffusion equation with zero initial condition. Therefore, by uniqueness, Uxxx = 0. Integrating this result thrice, obtain u(x, t) = A(t)x² + B(t)x+ C(t). Finally, it's easy to solve for A, B, and C by plugging into the original problem.

Q: Find a general solution to the given Cauchy-Euler equation for t > 0. 2d²y + dy dt +4t -28y = 0 dt…

A: Solution :

Q: Solve the initial value problem with x'(t) = A, for t≥0 with x(0) = Classify the nature of the…

A:

Q: 3. Let's study the ODE y" -y=t, y(0) = 0, y'(0) = 0. Find the transfer function (so, the form in the…

A: Given: An ordinary differential equation (ODE) defined as .Subjected to the initial conditions of…

Q: Exercise 3. A WSS process X(t) with autocorrelation function Rx(+) = e-+2/(207) is passed through an…

A: We have to find the values with the help of Hilbert transformation.

Q: Find the function y₁ of t which is the solution of 100y" - 9y = 0 with initial conditions y₁ (0) =…

A:

Q: Consider the following Linked List object called myList with the following nodes: 10- 20 -> 30 -> 40…

A: The given LinkedList object by the name myList has the following data. 10 -> 20 -> 30 -> 40…

Q: Find the transfer function G(z) of following difference equation and also find the impulse response…

A: As per the question we are given the difference equation of a system as : 10yk+1 + 5yk = 100xk+1…

Q: Find the function y₁ of t which is the solution of with initial conditions Y1 = 4y" + 36y' + 32y = 0…

A: Given differential equations is  4y"+36y'+32=0 It can be written as y"+9y'+8=0

Q: Given y = , y (0) = 1, h = 0.5. Find y (2) using the fourth-order RK

A:

Q: Integrate the following functions: 1.1) x-1 (2x + 7)-1 Hint: Use Partial Fractions before…

A:

Q: Exercise 3. A WSS process X(t) with autocorrelation function Rx(+) = e-2/(207) is passed through an…

A: The objective of this question is to find the cross-spectral density Sxy(w), the cross-correlation…

Q: Write a program in MATLAB to numerically solve for the concentration distribution in a duct of…

A: note :Since you have posted multiple questions, we will provide the solution only to the first…

Q: (5) Consider the Adams-Bashforth method wo = a; wi = a1; Wi+1 = Wi + 5 (3f(t;, wi) – f(i;-1, Wi-1)]…

A: Given: The Adams -Bashforth method , w0=α1; w1=α1; wi+1=wi+h23fti,wi-fti-1,wi-1to solve the equation…

Q: ty" - 2ty' + 2y = 5t², t > 0, y₁(t) NOTE: Use c₁ and ce as arbitrary constants. =

A:

Q: Q5) Answer the Following: 1- Solve the separable DE: dy -x² dx y² A a gortain

A: Given differential equation : dydx=-x2y2

Q: The values of mass m, spring constant k, dashpot resistance c, and force f(t) are given for a…

A:

Q: Suppose that a metal rod of length 40 cm is heated to a temperature of egrees Celsius, and the ends…

A: According to Bartleby guidelines I have solved first three parts. For remaining parts you can repost…

Q: (5) Solve the diffusion equation with dissipation: U - Dugr = bu, -0 <x < ,0 <t <0 with initial…

A: A general diffusion equation with constant dissipation with initial condition is of the form:…

Q: Match the second order linear equations with the Wronskian of (one of) their fundamental solution se…

A:

Q: Which of the following functions V(y1, y2) is a Lyapunov function for the dynamical system with…

A:

Q: homogeneous linear system of D. E.

A: We have to solve the given differential equations. dx1(t)dt=x1+x2+3x3dx2(t)dt=2x2+2x3dx3(t)dt=3x3

Q: 1. Consider the following second order linear equation with initial conditions (IVP): e'y" + y – y =…

A: Linear equation can be represented as,                                                         x→' =…

Q: 4. (Cole-Hopf transformation). Show that if o satisfies the heat equation then the change of…

A:

Q: In Exercises 59 and 60, two linearly independent solutions y₁ and y2 are given to the associated…

A: Step 1:Step 2:Step 3: Step 4:

Q: 4. Solve the diffusion problem, a'u = u,, 00, using separation of variables subject to the following…

A:

Q: Solve the first order PDE (1+y²) uz + Uy = 0, u(x,0) = e-r²

A:

Q: Use the method of variation of parameters to find a particular solution of the DE…

A:

Q: Solve the initial value problem with [3] Classify the nature of the origin as an attractor,…

A:

Q: Q2/ Find the error steady-state at (t ), where the system transfer function is G(s) = solve by…

A: Given function is, Gs=1s+3s+2. Convolution theorem in inverse Laplace : If, L-1f¯s=ft and L-1g¯s=gt…

Q: Solve the diffusion equation Ut = kurr, on the half-line 00, with initial and boundary conditions…

A:

Q: The method of reduction of order (Section 3.4) can also be used for the nonhomogeneous equation y" +…

A:

Q: Which of the following functions V(y₁, y2) is a Lyapunov function for the dynamical system with…

A:

Q: In Exercises 1 and 2, we consider the system dx 2x + 2y %3D dt dy = x + 3y. dt For the given…

A: Disclaimer: Since you have asked multiple question, we will solve the first question (Ex 1) for you.…

Q: Sa' = (2 – x)(y – æ) %3| = y – 2x – 2 The system can be linearized at the critical point (-2,-2) to…

A:

Q: Make a program in matlab that graphs the solution of the partial differential equation   with…

A: As per the question we are given an initial value problem which we have to numerically solve using…

Q: 1 (s) T(s) 4. For the rotational system shown, solve for G(s) = 100 DL

A:

Q: , Which of the following processes is stationary? A) An MA(1) process with 0 = -1.6 B) Y, = 58.46 +…

A: The stationary process is