Solve these practice questions on Ordinary and Higher Order Differential Equations.

Q1) Write a mathematical model, the solution of which will provide time t during that the water flows out of an opening 0.5 cm2 at the bottom of a conic funnel 10 cm high, with the vector angle .

Q2) Solve the following differential equations:

Q3) Solve .

Q4) Solve .

Q5) Solve

Q6) When a chicken is removed from the oven, its temperature is measured at 300oF. Three minutes later its temperature is 200oF. How long will it take for the chicken to cool off to a room temperature of 70oF.

Q7) Suppose that we have an artifact, say a piece of fossilised wood, and measurements show that the ratio of C-14 to carbon in the sample is 37% of the current ratio. Let us assume that the wood died at time 0, then compute the time T it would take for one gram of the radioactive carbon to decay this amount.

Q8) Solve the following differential equations:

Q9) Solve the following equations:

The next round of questions will be on Partial Differential Equations.