Anyone able to explain Differential Equations

Assignment Instructions: For each problem, be sure to show all steps for arriving at your solution. Work within this document. Use an equation tool as needed, and submit everything in one file.

1. Solve the following differential equation, showing all work. Verify the solution you obtain.

1. Solve the following initial value problem, showing all work. Verify the solution you obtain.

1. Using the Newton’s second law model for a vibrating spring with damping and no forcing,

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find the equation of motion if kg, kg/sec, kg/sec2, , and m/sec. What is the position of the mass after 1 second? Show all work.

1. A brine solution of salt flows at a constant rate of 6 L/min into a tank that initially held 50 L of brine solution into which was dissolved 1.5 kg of salt. The solution in the tank is stirred and flows out of the tank at the same constant rate of 6 L/min. If the concentration of the salt entering the tank is 0.05 kg/L, develop the differential equation that models this scenario and find an expression for the mass of salt, S (t ), in the tank at time t minutes. Use that function to find the amount of salt in the tank after 10 minutes. Show all work.