When a raindrop falls, it increases in size and so its massat time t  is a function of t , m(t) . The rate of growth of themass is km(t) for some positive constant . When weapply New ton’s Law of Motion to the raindrop, we get (mv)' = gm, where is the velocity of the raindrop(directed downward) and g is the acceleration due to gravity.The terminal velocity of the raindrop is lint→∞ v(t) . Find anexpression for the terminal velocity in terms of  g and k .

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A: Leibnitz integral rule.

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Q: Find the general solution of the differential equation and check the result by differentiation. (Use…

A:

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A: Differential equation formation

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A: I am attaching image so that you understand each and every step.

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A:

Q: Find the nth-order differential of the function y=2x.

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A:

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Q: DETERMINE THE INSTANTANEOUS RATE OF CHANGE OF THE FUNCTION AT X=1 sin (2³) 1 + √t - f(x) = x3 dt

A:

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.