Find the Exact length of the curve.

$x={e}^{t}+{e}^{-t},y=5-2t$ between $0\le t\le 3$

Carol Gates
2021-09-11
Answered

Find the Exact length of the curve.

$x={e}^{t}+{e}^{-t},y=5-2t$ between $0\le t\le 3$

You can still ask an expert for help

Faiza Fuller

Answered 2021-09-12
Author has **108** answers

To find:

asked 2021-02-04

Find the inverse Laplace transforms of the functions given. Accurately sketch the time functions.

a)$F(s)=\frac{3{e}^{-2s}}{s(s+3)}$

b)$F(s)=\frac{{e}^{-2s}}{s(s+1)}$

c)$F(s)=\frac{{e}^{-2s}-{e}^{-3s}}{2}$

a)

b)

c)

asked 2022-01-28

How to solve for the equation
y′′′+4y′′+5y′+2y=10cost
using laplace transform method given that
y(0)=0,y′(0)=0,and y′′(0)=3

asked 2022-01-18

Is there a closed form for any function f(x,y) satisfying:

$\frac{df}{dx}+\frac{df}{dy}=xy$

asked 2021-02-19

Solve the differential equation using Laplace transform of

${y}^{\u2033}-3{y}^{\prime}+2y={e}^{3t}$

when y(0)=0 and y'(0)=0

when y(0)=0 and y'(0)=0

asked 2022-01-21

A simple question about the solution of homogeneous equation to this differential equation

Given that$t,1+t,{t}^{2},-t$ are the solutions to $y{}^{\u2034}+a\left(t\right)y{}^{\u2033}+b\left(t\right)y{}^{\u2033}+c\left(t\right)y=d\left(t\right)$ , what is the solution of homogeneous equation to this differential equation? What i have done is tried the properties of linear differential equation that

$L\left(t\right)=L(1+t)=L\left({t}^{2}\right)=L(-t)=d\left(t\right)$ so the homogeneous solution should be independent and i claim that $1,t,{t}^{2}$ should be the solution. However, i am not sure hot can i actually conclude that these are the solutions? It seems that it can be quite a number of sets of solution by the linearity.

Given that

asked 2022-01-17

How to deal with two interdependent integrators?

I have two functions, f(t,x) and g(t,u), where$\frac{d}{dt}u=f(t,x)\text{}\text{and}\text{}\frac{d}{dt}x=g(t,u)$ .

I am trying to discretize the integral of this system in order to track x and u. I have succeeded using Euler integration, which is quite simple, since x(t) and u(t) are both known at t:

$u(t+h)=u\left(t\right)+hf(t,x\left(t\right))$

$x(t+h)=x\left(t\right)+hg(t,u\left(t\right))$

However, I am now trying to implement mid-point integration to get more accurate results. (Eventually Runge-Kutta but I am stuck here for now.)

I have two functions, f(t,x) and g(t,u), where

I am trying to discretize the integral of this system in order to track x and u. I have succeeded using Euler integration, which is quite simple, since x(t) and u(t) are both known at t:

However, I am now trying to implement mid-point integration to get more accurate results. (Eventually Runge-Kutta but I am stuck here for now.)

asked 2020-11-07

Write down the qualitative form of the inverse Laplace transform of the following function. For each question first write down the poles of the function , X(s)

a)$X(s)=\frac{s+1}{(s+2)({s}^{2}+2s+2)({s}^{2}+4)}$

b)$X(s)=\frac{1}{(2{s}^{2}+8s+20)({s}^{2}+2s+2)(s+8)}$

c)$X(s)=\frac{1}{{s}^{2}({s}^{2}+2s+5)(s+3)}$

a)

b)

c)