8. A tank initially contains 200 L of pure water. Brine with a salt concentration of 0.1 kg/L enters the tank at a rate of 5 L/min, and the mixed solution drains out of the tank at the same rate. (a) Set up a differential equation that models this situation, where y(t) is the amount of salt in the tank after t minutes. (b) Solve this differential equation to find y(t), the amount of salt in the tank after t minutes.

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A: In the question it is asked to solve the differential equations with initial values given.

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A: The initial conditions we have are  Initially, tank has 200 litres of freshwater. i.e.  V(t=0) = 200…

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A:

Q: 24.Use separation of variables to solve the differential equationdQ/dt=r(a+bQ),Q(0)=Q0, where a, b,…

A: dQdt=ra+bQ ,  Q0=Q0 By separating the variables, we get dQa+bQ=r dt Now integrating on both sides,…

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A: The detailed solution of the problem follow the next steps.

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A:

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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.