Prob. 1. Solve the differential equation dx dt =-2r +12r²-20r+8.5 over the time interval of [0, 4] with the step size of

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Prob 1 Solve The Differential Equation Dx Dt 2r 12r 20r 8 5 Over The Time Interval Of 0 4 With The Step Size Of 1 (21.77 KiB) Viewed 34 times

Prob. 1. Solve the differential equation dx dt =-2r +12r²-20r+8.5 over the time interval of [0, 4] with the step size of 0.5 and x(0)=1. (a) Use Euler's method. (b) Use the fourth-order Runge-Kutta method. (c) Calculate the exact solution of x(1). (d) Output your results for each method in a table format with two columns of time t and x(t). Plot the results of (a)-(c) versus time in one figure using different line styles or colors. Everything must be coded in one program.