Q1. Given the functional t2 I(x, y) = (9x²y 2y²x) dt t1 where i dx/dt, y = dy/dt, t and t2 are certain constant times. (a) Find the curve y(x) that minimizes I(x,y). (b) If x(t) = 2, and x(t,) = 1, use the results in (a) to obtain y(t) and y(t,). %3D (c) Use your results in (a) and (b) to evaluate the minimum value of I(x, y).

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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.