1. A differential equation linear if it can be expressed as L(x) = f(t) where L is a linear operator, i.e. satisfying L(a x + y) = aL(x) + L(y) for any variables x , y dx and constant a. Show that 3 dt + 4x – 3t = t2 is linear by identifying L and f and %3D proving that L is linear. L(x) = f (t) =

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Q: xy dx + (x² – 3y) dy = 0. %3D

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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.