Consider the ODE in problem 2 subject to the boundary conditions. dy (0) = 2, (1)...

  

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Consider the ODE in problem 2 subject to the boundary conditions. dy (0) = 2, (1) = -2. Solve the boundary value problem (BVP) using the Matlab functions bvp4c and ode45. Using some of the work in obtaining the analytical solution to problem 2, establish that the analytical solution the BVP is y(x) (5.7e-0.7e-² + 4x-3). Provide either a plot of y(r) for 0 <r < 1 or values of y(a) at æ = 0.2, 0.4, 0.6, 0.8, and 1 (numerical and analytical solutions). 2. [28 points] Solve the ordinary differential equation (ODE) d'y (-) = (2²-42+1), 0<r <1 subject to the initial conditions (0) = 2,(0) = 1, using the Matlab function ode45. Establish that the analytical solution to the initial value problem is y(x) = (4e +² - ² + 4x-3). Provide either a plot of y(r) for 0<x<1 (obtained using ode45) or values of y(r) at r = 0.2, 0.4, 0.6, 0.8, and 1 (numerical and analytical solutions). Consider the ODE in problem 2 subject to the boundary conditions. dy (0) = 2, (1) = -2. Solve the boundary value problem (BVP) using the Matlab functions bvp4c and ode45. Using some of the work in obtaining the analytical solution to problem 2, establish that the analytical solution the BVP is y(x) (5.7e-0.7e-² + 4x-3). Provide either a plot of y(r) for 0 <r < 1 or values of y(a) at æ = 0.2, 0.4, 0.6, 0.8, and 1 (numerical and analytical solutions). 2. [28 points] Solve the ordinary differential equation (ODE) d'y (-) = (2²-42+1), 0<r <1 subject to the initial conditions (0) = 2,(0) = 1, using the Matlab function ode45. Establish that the analytical solution to the initial value problem is y(x) = (4e +² - ² + 4x-3). Provide either a plot of y(r) for 0<x<1 (obtained using ode45) or values of y(r) at r = 0.2, 0.4, 0.6, 0.8, and 1 (numerical and analytical solutions).

Answer rating: 100% (QA)

x yexact yode45 0 2 2 02 225632577047210 225632576746533 04 261310488178383 261310488131377 06 30573... View the full answer