Let the following equation :  d2y/dt2 + t2 dy/dt + 3y = t with y(0) = 1 and y'(0) = 2 (t is real and positive)   (I) Using the Runge-Kutta method with a step delta(t) = 0.001, solve the equation for t[0,100] with a unit step. (ii) Give the graphical representation of the solution (iii) Give the graphical representation of y '(t) with respect to y (t) for t [0,100]

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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.