6. Find the largest interval for which the following initial value problems are guaranteed to have a unique solution. Explain your reasoning DO NOT SOLVE THE EQUATIONS. (a) Say" + 6x²y" + 4xy' – 4y = 0 ly(5) = 5, y'(5) = 8, y"(5) = 16 %3D (b) St(t – 2)y(4) + e2ty" + 8t²y = 0 y(1) = y'(1) = 1, y"(1) = 0 -

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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.