Demand for a certain kind of SUV obeys the following equation, D(x,y) = 16,000 – Vx – 15(0.4y – 10)3/2 where x is the price per car in dollars, y is the cost of gasoline per litre, and D is the number of cars. Suppose that the price of the car and the price of gasoline t years from now obey the following equations: x = 53,200 + 300t, y = 135 + 5V7 What will the rate of change of the demand be (with respect to time) 2 years from now?

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Q: (x² + 4) dy 山 3. y(2) = 0

A: we know that ∫dxx2+a2=1atan-1xa+C,  where a>0 see below the answer and calculation

Q: solve the Initial Value Problem using Separation of Variables. y' = xy2, y(1) = 2

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A: you can clearly understand if you follow the below solution

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Q: 1. Eliminate the arbitrary constants on the given equation: y = A + Be*

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Q: A 200-gal tank is half full of distilled water. At what time (t) = 0, a solution containing 0.5…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.