2. A tank contains 300 liters of fluid in which 30 grams of salt are dissolved. Brine containing 4 grams of salt per liter is then pumped into the tank at a rate of 3 L/min . The well mixed solution is pumped out at the same rate. Set up an initial value problem (a differential equation with an initial condition) to find the amount of salt Q(t) in the tank at any time t. (Do not solve the equation).

Q: 2. Show that y = e-6t satisfies the differential equation y" – y – 42y = 0.

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Q: 4. Eliminate the arbitrary constant 'a' in the differential equation: y – 2ay' + x2 = a? %3D

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A: Given: RdQdt + QC=E The given equation can be written as dQdt +QC=ER

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Q: i. Determine the general solution of the above differential equation.

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Q: 7. A 200-litre tank initially contains 100 litres of water with a salt concentration of 0.1 grams…

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Q: What is the solution of the first order differential equation y(k + 1) = y(k) + 5.

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A: hello greetings from bartelby.i am here to help you.

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Q: 1.) Find the general solution to the first order differential equation given below. -3x 3xe 2x y' 4y

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Q: Suppose that the population P(t) of a country satisfies the differential equation dP/dt= kP(200 - P)…

A: dPP(200-P)=kdt∫dPP(200-P)=k∫dt1200∫dPP-∫dP200-P=k∫dtInP-In(200-P)=200kt+cInP200-P=200kt+cP200-P=ce20…

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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.