Please help Find the solution to the initial value problem: x(0)-0x(O)--1 x(t) write x(t) as a product of a sine and a cosine, one with the beat (slow) frequency (μ-2)/2 , and the other with the carr...
Find the solution y of the initial value problem 3"(t) = 2 (3(t). y(1) = 0, y' (1) = 1. +3 g(t) = M Solve the initial value problem g(t) g” (t) + 50g (+)? = 0, y(0) = 1, y'(0) = 7. g(t) = Σ Use the reduction order method to find a second solution ya to the differential equation ty" + 12ty' +28 y = 0. knowing that the function yı(t) = + 4 is solution to that...
Consider the following initial value problem: dy = sin(x - y) dx, y(0) 1. Write the equation in the form ay = G(ax +by+c), dx where a, b, and c are constants and G is a function. 2. Use the substitution u = ax + by + c to transfer the equation into the variables u and x only. 3. Solve the equation in (2). 4. Re-substitute u = ax + by + c to write your solution in terms...
1. Find the particular solution of the differential equation dydx+ycos(x)=2cos(x)dydx+ycos(x)=2cos(x) satisfying the initial condition y(0)=4y(0)=4. 2. Solve the following initial value problem: 8dydt+y=32t8dydt+y=32t with y(0)=6.y(0)=6. (1 point) Find the particular solution of the differential equation dy + y cos(x) = 2 cos(z) satisfying the initial condition y(0) = 4. Answer: y= 2+2e^(-sin(x)) Your answer should be a function of x. (1 point) Solve the following initial value problem: dy ty 8 at +y= 32t with y(0) = 6. (Find y as...
Problem 1: Find the Laplace transform X(s) of x(0)-6cos(Sr-3)u(t-3). 10 Problem 2: (a) Find the inverse Laplace transform h() of H(s)-10s+34 (Hint: use the Laplace transform pair for Decaying Sine or Generic Oscillatory Decay.) (b) Draw the corresponding direct form II block diagram of the system described by H(s) and (c) determine the corresponding differential equation. Problem 3: Using the unilateral Laplace transform, solve the following differential equation with the given initial condition: y)+5y(0) 2u), y(0)1 Problem 4: For the...
Can you do this on MATLAB please? Thanks. (1) [20 pts] Find the exact solution to the Initial Boundary- Value problem utV x E (0,1), t>0, a(0, t)=0, a(i, t) = 0, t>0, t 20. Write the scheme and a code (forward in time, center in space) to approximate the solution of this prob- lem for u = 1/6. Take ΔⅡ 0.1 and compare your results with the exact solution at t = 0.01, 0.1, 1, 10 with At0.01 (1)...
please provide me with full working solution. Any help is appreciated. thank you in advance Consider the diffusion equation, au(x,t u(x,t) Here u(x,t) > 0 is the concentration of some diffusing substance, the spatial variable is x, time is t and D is a constant called the diffusivity with dimensions [LT-11. We will consider the diffusion equation on a finite spatial domain (0<x< 1) and an infinite time horizon (t > 0). To solve the diffusion equation we must include...
help with all except numbers 21-26 16. Solve the differential equation by using the Cauchy-Euler Equation 17. Find the solution to the given Initial Value Problem using Green's Theorem 0,y'(0)s 0 y(0) y" + 6y' + 9y x, 18. Find the solution to the given Boundary Value Problem y" ty-1, y(O)0, y(1) 19. Solve the system of differential equations by systematic elimination. dy dt dt 20. Use any procedure in Chapter 4 to solve the differential equation subjected to the...
Problem Thre: 125 points) Consider the following initial value problem: dy-2y+ t The y(0) -1 ea dt ical solution of the differential equation is: y(O)(2-2t+3e-2+1)y fr exoc the differential equation numerically over the interval 0 s i s 2.0 and a step size h At 0.5.A Apply the following Runge-Kutta methods for each of the step. (show your calculations) i. [0.0 0.5: Euler method ii. [0.5 1.0]: Heun method. ii. [1.0 1.5): Midpoint method. iv. [1.5 2.0): 4h RK method...
help please! thank you! (a) Show that an members of the family y-ve-1ฐ are-lutkn-ed Medaterntial mpalii (b) Use part (a) to find a fornvula for the solution to the ini- tial value problem v (0)-2. Then, sketch your solution on the slope field shown to the right. 2. Figure 1. Slope field for 3. (a) Show that all members of the family yarlutions of the disferential equation (b) Find the solution to the initial value problem ry'-tra-Zy·y(1)-S. 4. For what...