What is largest interval in which a unique solution is exist

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Reference no: EM131015330

1. Consider the initial value problem (x + 5) y' + {2 / x-π) y= In x, y(1) = -10. Without solving the equation, what is the largest interval in which a unique solution is guaranteed to exist?

2. A fish tank is initially tilled with 400 liters of water containing 2g/liter of dissolved oxygen. At t 0. oxygenated water containing 10 g liter of oxygen flows in at n rate of 4 liter min. live well-mixed water is pumped out at a rate of 3 liter min from the tank. Write an initial value problem (do not solve) that describes. Q(t). the amount of dissolved oxygen in the tank at any time r > 0 (until the time when the tank, eventually, overflows).

3. Newton's Law of Cooling says that the rate at which the temperature of a body changes is proportional to the difference of the temperature of the body and the temperature of the surrounding medium. Suppose a cup of coffee at 100^o C is placed in a room where the temperature is 25^o C. Write an initial value problem (do not solve) to describe the temperature of the cup of coffee at any lime t > 0.

Reference no: EM131015330

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What is largest interval in which a unique solution is exist : Consider the initial value problem (x + 5) y' + {2 / x-π) y= In x, y(1) = -10. Without solving the equation, what is the largest interval in which a unique solution is guaranteed to exist?

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