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. 

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Mechanical Engineer by education, Entrepreneur by heart. Day by day nothing is changing but when we look behind, everything is different.

Sol to Q9

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Mechanical Engineer by education, Entrepreneur by heart. Day by day nothing is changing but when we look behind, everything is different.

Sol Q7

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Mechanical Engineer by education, Entrepreneur by heart. Day by day nothing is changing but when we look behind, everything is different.

Sol to Q6

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Mechanical Engineer by education, Entrepreneur by heart. Day by day nothing is changing but when we look behind, everything is different.

Sol Q3 and 4

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Mechanical Engineer by education, Entrepreneur by heart. Day by day nothing is changing but when we look behind, everything is different.

Sol Q2 (ii)

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Mechanical Engineer by education, Entrepreneur by heart. Day by day nothing is changing but when we look behind, everything is different.

Sol to Q2 (i)

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Mechanical Engineer by education, Entrepreneur by heart. Day by day nothing is changing but when we look behind, everything is different.

Sol to Q1.

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A mechanical engineer trying to convert DREAMS into REALITY.

Q.7 Half life value is missing.

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A mechanical engineer trying to convert DREAMS into REALITY.

Q.8 (1)

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A mechanical engineer trying to convert DREAMS into REALITY.

Q.6

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A mechanical engineer trying to convert DREAMS into REALITY.

Q.2 (1cont) (2) (3)

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A mechanical engineer trying to convert DREAMS into REALITY.

Q.2 (1)

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Q 6 not finite sol

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