5. Suppose a cylindrical container containing a fluid has a drain on its side. Torricelli's law...

 

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5. Suppose a cylindrical container containing a fluid has a drain on its side. Torricelli's law states that the change in height of the fluid above the middle of the drain is proportional to the square root of the height of the fluid above the middle of the drain. Let h(t) denote the height of the fluid above the middle of the drain. Determine a differentiasl equation in h(t) that models Torricelli's law. Be sure to define all variables and parameters. 6. Solve the Ordinary Differential Equation. a) y' = t + 3 b) x = c) y = 6 sin(3t) e-1 5. Suppose a cylindrical container containing a fluid has a drain on its side. Torricelli's law states that the change in height of the fluid above the middle of the drain is proportional to the square root of the height of the fluid above the middle of the drain. Let h(t) denote the height of the fluid above the middle of the drain. Determine a differentiasl equation in h(t) that models Torricelli's law. Be sure to define all variables and parameters. 6. Solve the Ordinary Differential Equation. a) y' = t + 3 b) x = c) y = 6 sin(3t) e-1