Numerical Solution of a Two-Point Boundary-Value Problem Construct a computer program that uses both the secant method and the Runge-Kutta method (that you developed in assignment #3) to obtain a numerical solution to the two-point boundary-value problem: x' =fit,x) = x + 0.09 x 2 + cos(10 t) differential equation x(0) +x(1)-3.0 y condition Starting with the initial guesses 0.7 and 1.0 for the (unknown) initial value, x(0), obtain an approximation to x(0) for the final solution, x(); such that the boundary condition is satisfied to within a tolerance of 10. Use a fixed stepsize of 0.025 (i.e., take 40 steps each time you integrate the differential equation from t-0 to t-1). Write your program so that the output shows the values of x(O). x(1). and x(0)+x(1)-3 (the error in satisfying the boundary condition) at the end of each iteration of the secant method. After the last iteration of the secant method, re-integrate from t-0 to t1 and print out the solution for x(t) over the range [0,1] Your solution for x() should resemble the solution plotted below. Also, your approximation to x(0) when you finish, should be roughly 0.7378743. -4 Numerical Solution of a Two-Point Boundary-Value Problem Construct a computer program that uses both the secant method and the Runge-Kutta method (that you developed in assignment #3) to obtain a numerical solution to the two-point boundary-value problem: x' =fit,x) = x + 0.09 x 2 + cos(10 t) differential equation x(0) +x(1)-3.0 y condition Starting with the initial guesses 0.7 and 1.0 for the (unknown) initial value, x(0), obtain an approximation to x(0) for the final solution, x(); such that the boundary condition is satisfied to within a tolerance of 10. Use a fixed stepsize of 0.025 (i.e., take 40 steps each time you integrate the differential equation from t-0 to t-1). Write your program so that the output shows the values of x(O). x(1). and x(0)+x(1)-3 (the error in satisfying the boundary condition) at the end of each iteration of the secant method. After the last iteration of the secant method, re-integrate from t-0 to t1 and print out the solution for x(t) over the range [0,1] Your solution for x() should resemble the solution plotted below. Also, your approximation to x(0) when you finish, should be roughly 0.7378743. -4