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- for this equation: y''-xy'+4y = 0, find the reccurance relation, use power series solutions x0 = 0 express a2, a3,a 4, a5 in terms of a1 or a1The population of a city (in millions) at time tt (in years) is P(t)=2.7e0.002tP(t)=2.7e0.002t, where t=0t=0 is the year 2000. When will the population double from its size at t=0t=0?A particle moves along the x-axis so that at time t≥0 its position is given by x(t)=2t3+3t2−36t+50. What is the total distance traveled by the particle over the time interval 0≤t≤5 ?
- a)Evaluate y at position x=0.5 b)Evaluate the derivative dy/dx at position x=0.5. c)Using your values from a) and b) form the Taylor's expansion of y at x=0.5, truncated to include the first 2 terms.Solve the initial value problem for y as a function of xCan you find the amount of salt A in the tank at any time t?
- The number N(t) of supermarkets throughout the country that are using a computerized checkout system is described by the initial-value problem, dN/dt=N(1-0.0005N), N(0)=1. How many supermarkets are expected to adopt the new technology when t = 10?A particle moves along the x axis with its position at time t given by x(t) = (t + a)(t - b) where a and b are constants and a ≠ b. For which of the following values of t is the particle at rest?Suppose a tank contains 60 gallons of pure water. A mixture consisting of 1 pound of salt per gallon is flowing into the tank at a rate of 2 gallons per minute, and the mixture is continuously stirred. Meanwhile, the brine in the tank is allowed to empty out the tank at the same time at a rate of 3 gallons per minute. If the tank is completely empty after 1 hour, Önd the amount of salt in the tank at any time t.