Solve the problem. dy dt = ky + f(t) is a population model where y is the population at time t and f(t) is some function to describe the net effect on the population. Assume k = .02 and y = 10,000 when t = 0. Solve the differential equation of y when ft) = 6t. (A y = -300t - 15,000 + 25,000e -02t B y = 300t - 15,000 + 25,000e -02t y = -300t - 15,000 + 25,000e 02t D y = 300t + 15,000 + 25,000e -.02t

Q: Von Bertalanffy's equation states that the rate of growth in length of an individual fish is…

A:

Q: Let S represent sales of a new product (in thousands of units), let L represent the maximum level of…

A: Introduction : Sales in math deals with rough estimating at times and it gives that big picture view…

Q: The amount of fish in a lake is modeled by the logistic equation: = 2y(4 – y). If a certain amount…

A: Given, Logistic model of the fish in the lake is y'=2y(4-y). rate of catching fish is h, then…

Q: Find the equilibria of the differential equation, and construct the phase plot: y' (y − 3)(y – 5).…

A:

Q: tank contains 90 kg c lution is mixed and c

A: Given, a tank contains 90 kg of salt and 1000 L of water. Pure water enters a tank at the rate of 10…

Q: certain drug is administered intravenously to a patient at the continuous rate of 10 milligrams per…

A: Introduction: In mathematics, differentiation is the process of determining the derivative, or rate…

Q: The initial concentration of phosphorous (C) in a waste water pond is 107 ppm, as against the…

A: Euler's Method: Consider y' = f(t, y) with step size h yn+1=yn+hf(tn, yn)where tn+1=tn+h

Q: For non-negative PP, look at the differential equation:  dP/dt=-0.1P(1-P/200)  What are the…

A:

Q: A student is solving a separable differential equation and gets this far: ly=(x²3)dx What is the…

A: Integration is used to determine the bigger value by adding all the small parts. While…

Q: The amount y of the drug Warfarin in a patient’s body after t hours satisfies the differential…

A: We have to find the time and the rate of dissipation of the drug increase or decrease.

Q: Select the third differential equation, dy=-x2+y+0.5, and set the initial values to xo = -2.1, Y0 =…

A:

Q: A tank drains at a rate described by the differential equation below. At what time (t) will the tank…

A:

Q: The population of a particular type of fish in a lake would grow logistically according to the…

A:

Q: dx(0) = 9. Solve the following differential equation with x(0) = 0 and dt 9x dr? ..... X(t) =…

A:

Q: 3 lim - 1 x² + x – 2) X-1

A: By L'Hospital 's Rule limx→1 (xx-1 - 3x2+x-2) =limx→1(x(x2+x-2)-3(x-1)(x-1)(x2+x-2))…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.