3) Condider the differential equation + +y = 0 . i) What is the characteristic polynomial for this ODE? ii) Find the roots of the characteristic polynomial. iii) Using these, write the general solution of the ODE. iv) If this equation were the equation of a harmonic oscillator, would it be for an undamped, damped, critical or overdamper harmonic oscillator? Explain why.

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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.