A culture initially has P0 number of bacteria. At 1 h the number of bacteria is measured to be 3/2P0. If the rate of growth is proportional to the number of bacteria P(t) present at time t. Use the differential equation to determine the time necessary for number of bacteria to triple.

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Q: Solve for homogenous differential equation (x + y)dx + 2xdy = 0

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A: A detailed solution is given below.

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A: We will find the equation of A(t) as following.

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Q: A constant-stirred tank reactor (CSTR), initially filled with 20 kg of salt, is diluted with enough…

A: dSdt = 180s +40 S = salt concentration = 20kg s = 1% of original amount = 1% of 20 = 0.02kg

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Q: The tank in the figure contains 4000 L of water in which initially 50 kg of salt is dissolved. Brine…

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A: The complete solutions are given below

Q: A culture initially has P0 number of bacteria. At 1 h the number of bacteria is measured to be…

A: given: A culture initially has P0 number of bacteria. At 1 h the number of bacteria is measured to…

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Q: Find the order and degree of the differential equation:

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Q: What does it mean for a function to be a solution to a differential equation?

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Q: A small cannonball with mass 9 kilograms is shot vertically upward with an initial velocity of 130…

A: we have m=9, v=130, k=0.0025, g=-9.8

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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.