Ordinary differential equations UE Past Papers Questions.

Write down the following series as a single series in terms of

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Determine the radius of convergence and interval of convergence of the  following power series

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Does the ordinary differential equation |x’|+|x|=0, have a general solution?

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Does the ordinary differential equation (x’)²=-4, have a real solution?

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If we drop a stone, we can assume air resistance (“drag”) to be negligible. Experiments show that under that assumption the acceleration of the motion is equal to, . State this as an ordinary differential equation for x, the distance fallen as a function of time t. Solve the ordinary differential equation to get the familiar law of free fall, .

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