Let the following equation d ^ 2y / dt ^ 2 + 0.5cos (y) dy / dt + sin (y) = 0 with y (0) = π / 2 and y '(0) = 1/2 (i) using π the runge-kutta method with u step Δt = 0.001π, solve the equation for tϵ [0; 4π] with a step of 0.5π unit. (ii) give the graphical representation of y (t) for tϵ [0; 4π]. (iii) give the graphical representation of y '(t) as a function of y (t) for tϵ [0; 4π].

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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.