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Given the mathematical model of a system: dtdy+5y=5t2+12 where y= Overall displacement of the system t= Time Solve the equation above and find the displacement

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Given the mathematical model of a system: dtdy+5y=5t2+12 where y= Overall displacement of the system t= Time Solve the equation above and find the displacement of the system over t=0 to 1 seconds with using step size of 0.5 seconds. Solve the problem numerically and use Heun's method. Initial condition, y=1, at t=0 Write a MATLAB program to verify your solution in problem-4. Submission requirements a) Copy-pasted MATLAB program b) Program output

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