QUESTION 1 a) Using the substitution z = y 2r +3, solve the following initial...

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QUESTION 1 a) Using the substitution z = y – 2r +3, solve the following initial value problem dy dr 2+ Vy- 2r+3, y(0) = 0. b) Solve the following Bernoulli equation dy + 4y : dr y/2 1+e* c) Initially 30 g of salt is dissolved in a mixing tank containing 200 € of water. A brine solution of salt with concentration 1 g/l is then pumped into the tank at a rate of 4 (/min. The well-mixed solution is pumped out at the same rate. The amount of salt, A(t) at time t > 0, in the tank can be modelled as dA A dt 50 i. Find A(t). ii. What is the salt concentration (g/e) of the solution in the mixing tank at t = 5 minutes. QUESTION 1 a) Using the substitution z = y – 2r +3, solve the following initial value problem dy dr 2+ Vy- 2r+3, y(0) = 0. b) Solve the following Bernoulli equation dy + 4y : dr y/2 1+e* c) Initially 30 g of salt is dissolved in a mixing tank containing 200 € of water. A brine solution of salt with concentration 1 g/l is then pumped into the tank at a rate of 4 (/min. The well-mixed solution is pumped out at the same rate. The amount of salt, A(t) at time t > 0, in the tank can be modelled as dA A dt 50 i. Find A(t). ii. What is the salt concentration (g/e) of the solution in the mixing tank at t = 5 minutes.