Ordinary differential equations questions.

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#	Question
1	If the population of a country triples in 50 years, in how many years will doubles if the rate of increase of the said population is proportional to the number of inhabitants?. Mathematical Calculation
2	Express the following physical statement in differential equation form: "Radium decomposes at a rate proportional to the amount present". Mathematical Calculation
3	Find the second order differential equation associated with the primitive $y=4Ae^{8x}+Be^{4x}$ Mathematical Calculation
4	Write down the guess for a particular solution to the given differential equation. Do not find the coefficients. $y^{'}+9y=7x+e^{-7x}-1$ Mathematical Calculation
5	Use the method of variation of parameter to find the general solution to $y^{'}+9y=9$ Mathematical Calculation
6	Write down the following series as a single series in terms of $(x-x_0)^n$ $xsum_{n=0}^{alpha }n^2a_{n+1}(x-2)^{n+3}$ Mathematical Calculation
7	Determine the radius of convergence and interval of convergence of the following power series $sum_{n=0}^{alpha }(n+1)!(x-5)^n$ Mathematical Calculation
8	Does the ordinary differential equation \|x’\|+\|x\|=0, have a general solution? Mathematical Calculation
9	Does the ordinary differential equation (x’)²=-4, have a real solution? Mathematical Calculation
10	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, $g=10ms^{-2}$ . 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, $x=0.5gt^2$ . Mathematical Calculation