Using the finite-difference method, using h=5, solve for the value of β (15) the function with boundary conditions β (0) = 5 and β (20) = 8; given in the first image below: *Hint: For this solution, you will arrive at 3 equations and 3 unknowns of βi. *Round-off final root value to at least 4 decimal places only. *Show complete solution; then summarize your answer using a table provided on the second image:

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.