17. An initial population, p, of 10000 bacteria grows in number according to the equation 4t p(t) = 1000( cos(7t) + t2 + 50), where t is in hours. Find the rate at which the population is growing after 1 h.

Q: Suppose a 1000L tank contains 400 L of fresh water at time t = 0. At that time, a salt water…

A: The solution of above question is written below.

Q: What is the solution to the differential equation if x = 1 at t = 0 and, dx/ dt = 0 at t = O?

A: dxdt=0  at t = 0 means that the slope of normal line passing through the point (1, 0) is 0.

Q: I Solve the differential equatons when X= (x+y) dx +(2xy+xh 3x) dy=o 1. Y= 2

A:

Q: b) Use Euler's method to obtain a numerical solution of the differential equation dy y = 4 - dx with…

A: given             y' = 4 - y/x     and y(1) = 3, we have to find

Q: Q.5.Suppose that a projectile is launched straight upwad from the initial position with initial…

A: Given data:- The given initial velocity, v0>0 The given differential equation, dvdt=-g1+ρgv2…

Q: Find a specific solution to the initial value problem. 1 dy sec x tanx when y co)= 1 dx- 4

A: Given that       {1/(5y4+2e2y)}dx - (1/secx.tanx)dy = 0

Q: Given the function y = x3 + x² + x + 10, suppose x increases from 1 to 1.1. Find the absolute error…

A: We will find out the required value of absolute and percentage error.

Q: A tank contains 50-liters of brine in which 20 grams of salt is dissolved. Pure water is being…

A: Given: Let the rate of pumping in, Rin = 5 L / min Let the rate of pumping out, Rout = 4 L / min

Q: 16. Suppose the radius r, height h, and volume V of a dh related to dt dV cylinder are functions of…

A: Given: A cylinder with radius, r and height, h. The formula for the volume (V) of the cylinder is…

Q: If N(x) = sin x – sin θ and D(x) = x – θ, find the limit of N(x)/D(x) as x approaches θ. (SOLVE BY…

A:

Q: 2. Consider the differential equation dy da = 3(2-y)(y+ 2). %3D If y(0)=1, then determine lim,-00…

A: We know that if the first order derivative of a differentiable function is positive (nagative) at a…

Q: Suppose that in a certain company, the relationship between the price per unit p of its product and…

A: Given,  In a certain company, the relationship between the price per unit P and the weekly sale y,…

Q: Suppose that a quantity y = y(t) increases at a rate that is proportional to the square of the…

A: Given that a quantity y=y(t) increases at a rate that is proportional to the square of the amount…

Q: 6. Write down the differential, dy, of y = e3x.

A: to find the differential of y=e3x

Q: Solve the following differential eyuation x 2+ 2y = x* e** y.

A:

Q: 4 If y = In(8+ x4), find the differential dy. Your answer will be in terms of x and dx. Enter dæ as…

A:

Q: dy/dx=x squre root of y for y doesnt equal 0 Solve the differential equation

A:

Q: Solve the initial value problems for y as a functionof x. (x2 + 4) dy/dx = 3, y(2) = 0

A: Given Data : Differential Equation x2+4dydx=3, y2=0                      1 The given initial value…

Q: The degree of the differential equation dy (2) =# log () is d'y 03 1 not defined 2.

A: The degree of the differential equation is represented by the power of the highest order derivative…

Q: Suppose that a certain population has a growth rate that varies with time and that this population…

A: First rearrange terms in the given ordinary differential equation  dyy=0.5+sint5dt since it is…

Q: Find the Bolution to Hhe initial value problem - Please Write the folution with the computer.

A: Solution of Linear Differential Equation with Constant Coefficients: The general form of linear…

Q: Suppose you have the differential equation: y' + p(x)y ln(y) = q(x)y. Prove that the substitution v…

A:

Q: Suppose that the heat conduction in a rod of length Lis described by the equation ku- hu, 0 0, at…

A:

Q: If the function y = A sin z + B cos a satisfies the differential equation y" + y – 2y = sin z for…

A:

Q: A useful new product is introduced into an isolated fixed population of 1,000,000 people, and 100 of…

A: If x denotes the number of people who adopted the product at time t, measured in then we have the…

Q: Suppose that a population grows according to the unlimited growth model described by the dy = 0.15y…

A:

Q: 2 Solvehe initial value problems below. dy dt

A: The general solution of a differential equation always contains a constant of integration. The…

Q: Suppose a pendulum with length LL (meters) has angle θθ (radians) from the vertical. It can be shown…

A: NOTE : As per Bartleby rules, only three parts have to be answered. Please upload other parts…

Q: 1. Suppose that y = x³ + 4x. Suppose we increase x from 3 to 3.02. Use differentials to estimate the…

A:

Q: The differential equation (3x²e" – 2x}dx + (x*e' -sin y}dy = 0 is exact because ƏN ƏM Qu20[>_30imh…

A: Topic:- differential equations

Q: 8. If y = xi, then the value of the differential dy as x changes from 16 to is (A) * (B) 5 (c) (D)…

A:

Q: If y = (1/2x)(sin(lnx)-cos(lnx)), find dy/dx.

A:

Q: Suppose that in a certain company, the relationship between the price per unit p of its product and…

A:

Q: When sugar is dissolved in water, the amount A that re- mains undissolved after t minutes satisfies…

A:

Q: Suppose that a certain population has a growth rate that varies with time and that this population…

A: Here is the Answer and Explanation

Q: Suppose that a population grows according to the unlimited growth model described by the…

A: We will find out the required size of population.

Q: 41. The trough in Figure 3 (dimensions in centimeters) is filled with water. At time t = 0 (in…

A:

Q: 1 Solve for the differential of y when y=sinzx, x=÷, and dx= - 3 A) B) 2 -- C) D)

A:

Q: Solve the initial value problems for y as a functionof x. (x2 + 1)2 dy/dx = √x2 + 1, y(0) = 1

A: x2+12dydx=x2+1⇒dydx=x2+1x2+12⇒dydx=1x2+132⇒dy=1x2+132 dx Now integrating on both sides, we get…

Q: 5. a) Determine whether the given differential equation is exact. (sin. x)" dy 1+cos y = 0. dx

A: Given: sinxdydx+1+2xcosy=0

Q: Determine the differential equation of the family of lines passing through the origin O ædx + ydy =…

A:

Q: which 20 grams of salt is dissolved. Pure water is being pumped into the tank at a rate of 5…

A:

Q: dy Solve the differential equation dx + y + x y with initial condition v(0) =-1 and 03x32 with step…

A: The given differential equation is, dydx=x2+y+xyy'=x2+y+xy The initial condition is y0=-1 So, x0=0…

Q: 2) If a particle is moving in a straight line, and its distance away from its starting place (in…

A:

Q: Given the initial condition y(0) = 5, find the particular solution of the equation e'y' – 4x = 0.…

A:

Q: dy 2. Find the particular solution to the differential equation = 8x3 + sin x if the solution dx…

A:

Q: show that the solution of the differential equation xdy−ydx =√x2 +y2dx  is sinh^−1(y/x)=lnx+C

A: According to the given information, it is required to solve the given differential equation:

Q: Solve the initial value problem dy y = 5e" + 28e5* dx with y(0) = 8.

A: The solution of differential equation is given as follows :

Q: (1/4) Estimate the value of 82 a. approximation b. differentials

A: To estimate the value of 8214 by using a approximationb differentials

Q: Determine the quadrants in which the solution of the differential equation dy/dx = (1/2)x2y is an…

A: Here given differential equation as dydx=12x2yordyy=x2dx2