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Calculus and Analysis

Differential equations

Consider the initial value problem for the equation of linear pendulum L. with a=0.6, b=1.7. Write this problem as an equivalent problem for a system of first-order equations. Find (analytically) the phase trajectory of this system passing through the given point (a,b). Write down the euler method for the system from

Laplace equation in cylindrical coordinates

In this problem, you will find the electrostatic potential inside an infinitely long, grounded, metal cylinder of unit radius whose axis coincides with the z-axis (See figure below). In cylindrical coordinates, the potential, V(r, theta, z), satisfies Laplace's equation... <i>Please see attached</i>... Let us assume that the po

Linear dependency, Wronskian and Bessel's Equation

Three problems regarding the Wronskian and solutions of a second order differential equation. Example of a question 1. Determine whether the following sets of functions are linearly dependant or independent... Please see attached. 2. Bessel's equation x²y" + xy' + (x² - n²)y = 0 where n is a constant, i

Conics, Parametric Equations, and polar Coordinates

Answers must be explained very clearly. Answers without proper justification will not be accepted. I am having a lot of trouble with these questions and the last time I posted this the TA just gave me a buch of BS. Please take your time and answer these questions clearly and acurately. Thanks See attached for problems

Differential Equations.

1) consider the equation (non-homogenous): <i> Please see attachment for equation. </i> ? find its general solution ? find the particular solution of this equation, satisfying the initial condition y(0)=0, y'(0)=0, y''(0)=0 2) find the general solution of the differential equation (non-homogeneous) <i> Please

Velocity of ping pong ball

**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

Differential Equation (DE); Initial Value Problem (IVP)

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.)

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?

Solving an IVP Long-Term Behaviour of the Solution

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

Integrating Factors

Use the five steps of the Method of Integrating Factors to find the general solution of each linear ODE (hint: write ODE in normal linear form): y' - 2ty = t y' = sin(t) + y*sin(t) (PLEASE SEE ATTACHMENT FOR COMPLETE PROBLEM)

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


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)