Consider the differential equation ty" + (-12t2 – 1)y' + 36t°y = 0, para t > 0. We know that the differential equation admits a solution of the form y(t) = e" for fixed r. Let y(t) be any solution to the differential equation. Regarding the behavior of the solutions regarding t → +o we can say that: a. lim t 2e-32 +3y(t) = u'(1) – 3y(1). %3D t+00 b. lim e 4+4y(t) = ty'(1) – y(1). t100 C. lim e 4t y(t) não está definido e lim e 5 y(t) = 0. 5t2 %3D t+00 t+00

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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.