## Differential Equations: differential equations – #27829

Question: Determine the value of r, if any, such that y=e^rx is a solution of the differential equations given below. a) y” + 6y’ + 9y = 0 b) y" – 5y’ + 6y = 0 c) y" – 3y’ +2y = 0 Related Posts:Differential Equations Solved ProblemsDifferential Equations: differential equations…Differential Equations: differential equations…Differential Equations:...

## Differential Equations: differential equations – #27830

Question: Use Euler’s method with the given step size (?x or ?t) to approximate the solution of the initial value problem over the standard interval. Present your answers as a table and as a graph a) \(\frac{dy}{dx}={{y}^{1/3}}\), y(0) = 1, 0 <_ x <_ 4, \(\Delta x\) = 0.5 b) \(\frac{dy}{dt}=\cos y\), y(0) = 1,...

## Differential Equations: differential equations – #27831

Question: A tank with a 1000-gal capacity initially contains 500gal of water that is polluted with 50lbs of particulate matter. At time t=0, pure water is added at a rate of 20gal/min and the mixed solution is drained off at a rate of 10gal/min. How much particulate matter is in the take when it reaches...

## Differential Equations: differential equations – #27234

Question: An object of 5 kg is released from rest 1000 meters above the ground level and allowed to fall under the influence of gravity. Assuming that the force due to air resistance is proportional to the velocity of the object with proportionality constant k = 50 kg/sec, determine the formula for the velocity of...

## Differential Equations: differential equations – #27832

Question: Polonium-210 is a radioactive element with a half life of 140days. Assume that 20 milligrams of the element are placed in a lead container and that y(t) is the number of milligrams present t days later a) Find the formula for y(t) b) How many milligrams will be present after 12 weeks? c) How...