Problem 1: The differential equation equation y (t) = sin(3t)y' (t) + (log(y(t) + 1)) with...

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Problem 1: The differential equation equation y" (t) = sin(3t)y' (t) + (log(y(t) + 1)) with boundary conditions y(0) = 0 and y(1) = 1 can be solved by using the initial conditions y(0) = 0 and y' (0) = s. By varing the parameter s and solving the equation numerically on [0, 1] we see that the value the numerical solution Y at 1 varies. Solve the initial value problem for at least 40 values of s between 0 and 1. For all of these solutions determine the value of the numerical solution at 1 and save it an array, say e. Find the sign change of the vector e - 1( i.e. find the index for which the signs of e- 1 change. You can use fzero.m) and compute and plot the solution of the equation corresponding value of e. Problem 1: The differential equation equation y" (t) = sin(3t)y' (t) + (log(y(t) + 1)) with boundary conditions y(0) = 0 and y(1) = 1 can be solved by using the initial conditions y(0) = 0 and y' (0) = s. By varing the parameter s and solving the equation numerically on [0, 1] we see that the value the numerical solution Y at 1 varies. Solve the initial value problem for at least 40 values of s between 0 and 1. For all of these solutions determine the value of the numerical solution at 1 and save it an array, say e. Find the sign change of the vector e - 1( i.e. find the index for which the signs of e- 1 change. You can use fzero.m) and compute and plot the solution of the equation corresponding value of e.

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