Consider the following ODE, which is a two-point boundary value problem: y(x) = 4y + x,...

Transcribed Image Text:

Consider the following ODE, which is a two-point boundary value problem: y"(x) = 4y + x, y (0) = 1, y(2) = 3. To solve it with shooting method, we let y(x) be the solution of y" (x) = 4ỹ + x, y (0) = 1, 5(0) = 1, and let 5(x) be the solution of j"(x) = 4ỹ + x, y (0) = 1, y(0) = 2. Let now y = àỹ + (1 – 2)ỹ. For what value of À will this y be the solution of the two point boundary value problem? 2- 5(2) (2) – 5(2) 1- y (2) (2) – 5(2)* 2- (2) = y (0) – y (0) 3 - 5(2) (2) – (2) Consider the following ODE, which is a two-point boundary value problem: y"(x) = 4y + x, y (0) = 1, y(2) = 3. To solve it with shooting method, we let y(x) be the solution of y" (x) = 4ỹ + x, y (0) = 1, 5(0) = 1, and let 5(x) be the solution of j"(x) = 4ỹ + x, y (0) = 1, y(0) = 2. Let now y = àỹ + (1 – 2)ỹ. For what value of À will this y be the solution of the two point boundary value problem? 2- 5(2) (2) – 5(2) 1- y (2) (2) – 5(2)* 2- (2) = y (0) – y (0) 3 - 5(2) (2) – (2)