A large tank originally contains 1000 litres in which 5 kilograms of salt is dissolved. Pure water is allowed to enter the tank at a rate of 16 litres per minute, and the well stirred mixture is allowed to flow out of the tank at a rate of 18 litres per minute. If A(t) is the amount of salt (in kilograms) in the tank at time t (in minutes), then which of the following initial value problems is satisfied by A(t)?

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

A: For statement

Q: Suppose a 1000 L tank contains 100 L of fresh water at time t = 0. At that time, a salt water…

A: The rate of change of a substance in a container is determined by the concentrations as well as the…

Q: The value C for the solution of the initial value problem f'(x) = x* 8z +4, given that f(0) = 0. %3D

A:

Q: What is the solution of the initial value problem given below with the initial condition y(0) = 16?…

A:

Q: Find the function f(x) described by the given initial value problem. f"(x) = 0, f'(-3) = -5, f(-3) =…

A:

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

A: For given statement

Q: Solve the Initial value problem x' -x=8(t-2),x(0) =x' (0) =0

A: We use the Laplace transform to solve the given initial value problem.

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

A:

Q: Directly using the Laplace transform

A:

Q: For the Initial Value Problem given below:

A: Given,                dydx+2y=2-e-4t, y(0)=1

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A:

Q: Use the Runge-Kutta method of order four to approximate the solution of the following initial-value…

A: Step:-1 Runge kutta Method of fourth order:- ti+1=ti + h Here, h is step size. xi+1=xi +16k1+2 k2 +2…

Q: Solve the given initial-value problem. X' X(t) %3D

A:

Q: We are given a initial value problem u" – 16u = 5t, u(0) = 0, u'(0) = 1 Solve the problem by using…

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Q: Determine if y=e−x+8x−9 is a solution to the initial value problem given by y′+1=8x−y and y(0)=−8.

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Q: What is the actual solution to the following Initial Value Problem? 2ty′+4y=3 ; y(1)=−4 what is the…

A:

Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

A: On integrating, we get

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

A:

Q: Solve the initial value problem below. x²y" – - 3ry' + 4y = 0, y(1) = F 3, y'(1) = – 1 y =

A: Homogeneous Linear differential equation :   An equation of the form…

Q: 1. Solve for y(t) for a given initial value problem as shown below: y" – 2y' + 5y 8etsin2t

A:

Q: Suppose a 50-gallon tank contains a volume V0 of clean water at time t = 0. At time t = 0, we begin…

A: (a) It is given that, a 50-gallon tank contains a volume V0 of clean water at time t = 0. At time t…

Q: Solve the following initial value problem by the 2nd order and 4th order Runge-Kutta methods,…

A:

Q: 1. Solve for y(t) for a given initial value problem as shown below:. y" – 2y' + 5y = 8etsin2t

A: The given differential equation is:y"-2y'+5y=8etsin2t

Q: In each of the following problems, find the solution of the given initial value problem. Sketch the…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Solve the given initial-value problem. x-( -(:) x-() X' = = X + %3D

A:

Q: Determine whether the following equation are separable. If so, solve the initial value problem. y…

A: ∫dxx=lnx+C∫exdx=ex+C

Q: Solve the initial-value problem. (dy)/(dx) = (5)/√(x), for x ≥ 1 with y(4) = 4 The solution to the…

A: we have the differential equation  dydx=5x with y(4) = 4 having the initial value problem

Q: Solve the higher order initial-value problem f''(x) = x-1/x + 3 ; f'(1) = 3, f(1) = 0

A:

Q: Find the function f(x) described by the given initial value problem.   f"(x)=0,  f'(-5)=-5,  f(-5)=2…

A: to determine.

Q: Solve the initial value problem below. y " +4y + 8y = 0, y (0) = 0 & y' (0) = 4

A:

Q: Find a formula for the solution of the initial value problem, and note that it is independent of λ.…

A: Given the equation:

Q: What is the actual solution to the following Initial Value Problem? 2ty′+4y=3 ; y(1)=−4

A:

Q: Find the real-valued solution to the initial value problem -3 x'(t) = x(0)

A: Given: X't=-32-1-1x and initial value is X0=1-2

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

A: x(t) is the amount of salt in grams in the solution at time 't'Rate of change of amount of salt in…

Q: Find the function f(x) described by the given initial value problem. f'(x) = 6", f(4) = 4 f(x) =

A: Given f'(x)=6x , f(4)=4 We have to solve f(x)

Q: Solve the following initial-value problem. (f) xy'''+2y'' = 6x with y(1) = 2, y'(1) = 1, and y''(1)…

A: Given differential equation xy'''+2y''=6x with y1=2, y'1=1 and y''1=4 Multiply by x2 in…

Q: 1. Solve for y(t) for a given initial value problem as shown below: y" – 2y' + 5y = 8etsin2t

A: Explanation of the answer is as follows

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

A:

Q: Solve the given initial-value problem. dx1 X1 (t) with x, (0) = - 3 and x2(0) = - 1. X2 (t) dt 3 12…

A:

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

A:

Q: Find the solution to the initial value problem as an explicit function of the independent variable.…

A: Given : (t2+1)y'+y2+1=0,   y(3)=2

Q: Solve the given initial-value problem. X' = 0 1 0 X, X(0) 1 0 0 X(t) =

A:

Q: Solve the initial value problem f'(x) = vx +,f(1) = 2.

A:

Q: Solve the initial value problem = e* + 4x – 3 where y = 5 when x = 0; that is, find y = f (x). dx

A:

Q: . Apply to the initial value problem y' = -xy + 1, y(0) = 0 three steps of the Picard-Lindelöf…

A:

Q: The position x(t) of an object of mass m that is attached to a vertical spring with constant of…

A:

Q: 2. Find the solution of the initial value problem and describe its behavior as t ∞ 9. 了, -1 -3 ) 7()…

A:

Q: Solve the given initial-value problem. x - (; -1 -2 3 4 x +(:), xco)- - ( ) X' = 6 X(t) :

A:

Q: If the function f(t) is a solution of the initial value problem y' = 5y - 5, y(0) = 3, find f(0) and…

A: Given differential equation is y' = 5y - 5 , y(0) = 3

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.