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What is a differential equation?

  1. Jan 12, 2009 #1


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    1. The problem statement, all variables and given/known data

    A skier of mass M is skiing down a frictionless hill that makes an angle θ with the horizontal. The skier starts from rest at time t = 0 and is subject to a velocity-dependent drag force due to air resistance of the form F = -bv, where v is the velocity of the skier and b is a positive constant. Express all algebraic answers in terms of M, b, θ , and fundamental constants.

    Write a differential equation that can be used to solve for the velocity of the skier as a function of time.

    2. Relevant equations

    I understand a differential equation involves calculus, but I don't know how to apply it.

    3. The attempt at a solution

    v = (mgsinθ - ma)/b
  2. jcsd
  3. Jan 12, 2009 #2


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    Try finding the resultant force, then use Newton's 2nd law with non-constant velocity, i.e. [itex]F=m \frac{dv}{dt}[/itex]
  4. Jan 13, 2009 #3

    Andrew Mason

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    You have written the correct differential equation already. In differential form it would be:

    [tex]m\frac{d^2s}{dt^2} = mgsin\theta - b\frac{ds}{dt}[/tex]

    A differential equation is just an equation containing differentials. The solution of these equations is often complicated. Certain techniques for solving them exist and are the subject of a course in differential equations.

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