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    Calculus and Analysis

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    Velocity Differential Equation

    **Just need help with question 3, answers for 1 and 2 are provided*** A ping-pong ball is caught in a vertical plexiglass column in which the air flow alternates sinusoidally with a period of 60 seconds. The air flow starts with a maximum upward flow at the rate of 7m/s and at t=30 seconds the flow has a minimum (upward) flow

    Limits and rate of change

    See attachment Suppose that a steel ball falls a distance at 16t^2 feet in t seconds. Find its average velocity from t=2 to t=4 seconds. A certain university has yearly enrollment as shown in the table. Find the average rate of change of enrollment (in students per year) from year 1998 to 2002.

    Critically damped harmonic motion

    This problem is an example of critically damped harmonic motion. A hollow steel ball weighing 4 pounds (mass = 1/8 slugs) is suspended from a spring. This stretches the spring 1/8 feet. The ball is started in motion from the equilibrium position with a downward velocity of 8 feet per second. The air resistance (in pounds) of the

    Harmonic motion

    A hollow steel ball weighing 4 pounds (mass = 1/8 slugs) is suspended from a spring. This stretches the spring 1/6 feet. The ball is started in motion from the equilibrium position with a downward velocity of 8 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per

    Damped harmonic motion ODE

    This problem is an example of critically damped harmonic motion. A hollow steel ball weighing 4 pounds (mass = 1/8 slugs) is suspended from a spring. This stretches the spring 1/8 feet. The ball is started in motion from the equilibrium position with a downward velocity of 8 feet per second. The air resistance (in pounds)

    Mechanical displacement

    A hollow steel ball weighing 4 pounds (mass = 1/8 slugs) is suspended from a spring. This stretches the spring 1/6 feet. The ball is started in motion from the equilibrium position with a downward velocity of 8 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet pe

    Euler-Cauchy Equation

    Consider the differential equation: r^2*R"+r*R'-R=0 a) Find all values of n for which the function R=r^n is a solution to the differential equation. Do this by substituting {the solution into the DE and seeing which values of n will make the equation true. b) Solve the initial-value problem (IVP) with R(1)=2 and R'(1)=0.

    Linear Differential Equations

    1) Consider the equation... ? Find its general solution. ? Find the particular solution of this equation satisfying the initial condition. 2) Find the general solution of the differential equation... ? Prescribe any concrete initial data for which this equation has a unique solution. ? Find the particular solution of th

    Differential Equations : Rate of Change Application Problem and Wronskian

    1) Miss X would like to take out a mortgage to buy a house in Leicester. The bank will charge her interest at a fixed rate of 6.1% per year compounded continuously. Miss X is able to pay money back continuously at a rate of £6000 per year. ? Make a continuous model of her economic situation, i.e. write a differential equatio

    Solve Three Differential Equations

    Find the general solution of the following system of differential equations: i.e. 1) dx/dt = x-2y-t2 (FOR COMPLETE PROBLEMS PLEASE SEE ATTACHMENT)

    Calculating Curl of F and Potential for various n values

    Please help with the following information. a) Calculate the curl of F=r^n*(xi+yj) b) For each n for which curlF=0 , find a potential g such that F=grad(g). (Hint: look for a potential of the form g=g(r), with r=sqrt(x^2+y^2). Watch out for a certain negative value of n which the formula is different.)

    Differential Equation and Water Leaks

    Leaky bucket: A bucket in the shape of a cylinder has a small hole in its bottom, through which water is leaking. Let the height of the water in the bucket be h(t), let A be the cross sectional area of the bucket and a the area of the small hole. We want to find out how long will it take the bucket to empty (see attachment for m

    Differential Equations and Mercury Levels in a Lake

    A lake contains 60 million cubic meters (2MCM) of water. Each year a nearby plant adds 8.5 grams of mercury to the lake. Each year 2MCM of lake water are replaced with mercury-free water. 1. What is the differential equation that governs the amount of mercury in the lake? 2. According to your differential equation how much m

    Solution to Nonlinear Differential Equation

    Please see the attached file for the fully formatted problems. 1. Consider the nonlinear differential equation attached a. Find the solution to this differential equation satisfying y(0) = y0 where y0 does not equal +/- 1. What is the solution if y0 = +/-1. b. What happens to the solution as t--> infinity for y0 > -1?

    First Order Differential Equation

    Problem: First find the general solution of the linear ODE in each IVP by following the steps of the procedure. Then use the initial condition to find the solution of the IVP. Discuss that solution's qualitative behaviour as t --> +(SYMBOL). Give the largest t-interval on which the solution is defined: y' + 2y = 3, y(0) = 1

    Ode (Boundary Condition, Implicit and Explicit Solutions)

    Consider the ODE y' = y2/x subject to the boundary condition y(1)=1. Find an implicit solution of the form H(x,y) = constant, then find an explicit solution of the form y=y(x). What is the largest x-interval on which the solution is defined? *(Please see attachment for proper citation of symbols and numbers)

    Differential Equations

    For each of the following ordinairy differential equations, indicate its order, whether it is linear or nonlinear, and whether it is autonomous or non-autonomous. a) df/dx +f^2=0 (See attachment for all questions)

    Multiple integrals

    Consider the vector field F(x,y)= (-yi+xj)/(x^2+y^2) Question1)Show that F is the gradient of the polar angle function teta(x,y)=arctan(y/x) defined over the right half-plane x>0 . Question2)Suppose that C is a smooth curve in the right half-plane x>0 joining two points : A:(x1,y1) and B(x2,y2).Express "integral(F.dr)"on

    Integral Equation Solved

    Please show me how to solve this equation - can it be solved by substitution or am I on the wrong track? *(Please see attachment for equation)