a) The displacement s of a body in a damped mechanical system, with no external forces, satisfies the following differential equation d²s ds +5=+ 6.25s = 0 dt2 dt where t represents time. If initially, when t = 0, s = 1 and = 3, solve the differential equation for s in terms of t.

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Q: (Dª – D³ – 3D² + D + 2)y = 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.