1. Questions

Calculus

Suppose that we use Euler's method to approximate the solution to the differential equation
𝑑𝑦/𝑑π‘₯=π‘₯^4/𝑦 𝑦(0.1)=1

Let 𝑓(π‘₯,𝑦)=π‘₯^4/𝑦.
We let π‘₯0=0.1 and 𝑦0=1 and pick a step size β„Ž=0.2. Euler's method is the the following algorithm. From π‘₯𝑛 and 𝑦𝑛, our approximations to the solution of the differential equation at the nth stage, we find the next stage by computing

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
FECK

  1. at (0.1 , 1 )
    slope = dy/dx = (0.1)^4 /1 = (10^-1)^4 = 10^-4
    at x = x + h = 0.1 + 0.2 = 0.3
    Using Euler
    our guess at y = 1 + h (dy/dx) = 1 + 0.2 * 10^-4 = 1 +0.00002 = 1.00002

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
    👤
    Damon

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    Consider the differential equation dy/dx = -1 + (y^2/ x). Let y = g(x) be the particular solution to the differential equation dy/ dx = -1 + (y^2/ x) with initial condition g(4) = 2. Does g have a relative minimum, a relative

  2. Calc

    Consider the differential equation dy/dx=-2x/y Find the particular solution y =f(x) to the given differential equation with the initial condition f(1) = -1

  3. calculus

    Below is the graph of f '(x), the derivative of f(x), and has x-intercepts at x = -3, x = 1 and x = 2 and a relative maximum at x = -1.5 and a relative minimum at x = 1.5. Which of the following statement is true? (it's a positive

  4. Calculus BC

    Let y = f(x) be the solution to the differential equation dy/dx=y-x The point (5,1) is on the graph of the solution to this differential equation. What is the approximation of f(6) if Euler’s Method is used given βˆ†x = 0.5?

  1. Calculus

    Consider the differential equation dy/dx = x^2(y - 1). Find the particular solution to this differential equation with initial condition f(0) = 3. I got y = e^(x^3/3) + 2.

  2. Calculus

    The general solution to the differential equation dy/dx=xy is y=±√(x^2+C). Let y=f(x) be the particular solution to the differential equation with the initial condition f(βˆ’5)=βˆ’4. What is an expression for f(x) and its

  3. I would like to understand my calc homework:/

    Consider the differential equation given by dy/dx=(xy)/(2) A) sketch a slope field (I already did this) B) let f be the function that satisfies the given fifferential equation for the tangent line to the curve y=f(x) through the

  4. calculus

    consider the differential equation dy/dx= (y - 1)/ x squared where x not = 0 a) find the particular solution y= f(x) to the differential equation with the initial condition f(2)=0 (b)for the particular solution y = F(x) described

  1. Calculus

    Suppose you throw an object from a great height, so that it reaches very nearly terminal velocity by time it hits the ground. By measuring the impact, you determine that this terminal velocity is -49 mi sec. A. Write the equation

  2. math

    Consider the differential equation dy/dx = x + 2y, with initial condition y(0) = 2. Use Euler's method with four steps to estimate y when x=1.

  3. Calculus - HELP URGENT PLEASE

    Consider a lake of constant volume 12200 km^3, which at time t contains an amount y(t) tons of pollutant evenly distributed throughout the lake with a concentration y(t)/12200 tons/km^3. assume that fresh water enters the lake at

  4. Calculus

    Consider the differential equation dy/dx = x^4(y - 2). Find the particular solution y = f(x) to the given differential equation with the initial condition f(0) = 0. Is this y=e^(x^5/5)+4?

View more similar questions or ask a new question.