Midterm Assessment

AMATH 250 Online

数学Midterm代考 You may use any of the content posted on the AMATH 250 Learn site and your recommended course note, but you are NOT…

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1.50 Recognize the linear and nonlinear difffferential equations. Justify your answers.

  1. Find the general solutions (implicit or explicit) to the following equations. 数学Midterm代考
  1. An object of mass m is dropped vertically from a height h0 about ground level with zero initial velocity. We are interested in its time flflight tf before hitting the ground. Suppose that we do not know any laws of physics but suspect that tf depends on m, h0, the acceleration due to gravity g, and the shape of the object characterized by a dimensionless number s. Use dimensional analysis to determine how tf depends on those other parameters. (The effffect of air drag is assumed to be incorporated into s.)
  2. Give a qualitative sketch of the solutions of

Hint: You do not need to solve the DE. First determine the intervals of increase/decrease and intervals of concavity, then sketch the qualitative shape of

the solutions.

  1. (a) For the following IVP, predict the behaviour using the Existence/Uniqueness Theorem.

(b) Solve the IVP from part (a). Your fifinal answer may include a defifinite integral.

  1. Consider the initial value problem For what value of α, the general solution y(t) approaches zero when t → ∞.