1. Questions

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 point (1,1). Then use your tangent line equation to estimate the value of f(1.2).
C) find the particular solution y=f(x) to the differential equation with the initial condition f(1)=1. Use your solution to find f(1.2).
D) compare your estimate of f(1.2) found in part b to the actual value of f(1.2)
E) was the estimate under or over? Use the slope field to explain why?

  1. 👍
  2. 👎
  3. 👁
Amber

  1. You need to have patience and not post the same stuff umpteen times. The tutors who concentrate on this type of math are not online yet.

    1. 👍
    2. 👎
    👤
    Writeacher

  2. Please do not keep posting the same question over and over. It's considered spamming and could get you banned from posting here.

    1. 👍
    2. 👎
    👤
    Ms. Sue

  4. B)
    at (1 , 1) dy/dx = slope = 1*1/2 = .5
    so
    y = .5 x + b is tangent for some b
    put in (1 , 1 )
    1 = .5 + b
    b = .5
    so tangent at (1,1) is
    y = .5 x + .5
    at x = 1.2
    y = .5(1.2) + .5 = 1.1
    ==========================
    C)
    dy/y = (1/2) x dx

    ln y = (1/4) x^2 + C
    y = k e^(x^2/4)

    1 = k e^(1/4)
    1 = 1.28 k
    k = .779

    y = .779 e^(x^2/4)
    at x = 1.2
    y = .779 e^(1.44/4)
    y = .779 * 1.433
    y = 1.116
    etc

    1. 👍
    2. 👎
    Damon

  5. Do not panic. Plug and chug.

    1. 👍
    2. 👎
    Damon

  6. I think the whole non panicing ship sailed a long time ago haha. Sorry and thanks for the help!

    1. 👍
    2. 👎
    Amber

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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

  2. 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

  3. 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 ∆x = 0.5?

  4. 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(−5)=−4. What is an expression for f(x) and its

  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/Math

    The slope field for a differential equation is shown in the figure. Determine the general solution of this equation. The slope field has positive slopes in quadrants 2 and 4 and negative slopes in quadrants 1 and 4. It looks like

  3. 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

  4. Math

    1. Use point-slope form to write the equation of a line that has a slope of 2/3 and passes through (-3, -1). Write your final equation in slope-intercept form. 2. Write the equation in standard form using integers (no fractions or

  1. 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?

  2. Math

    1. Find the slope of the line that passes through the points (-1, 2), (0, 5). 2. Suppose y varies directly with x, and y = 15 and x = 5. Write a direct variation equation that relates x and y. What is the value of y when x = 9? 3.

  3. Calculus!!

    Consider the differential equation given by dy/dx = xy/2. A. Let y=f(x) be the particular solution to the given differential equation with the initial condition. Based on the slope field, how does the value of f(0.2) compare to

  4. Math

    Write an equation of the line that passes through the given points. (-1,5) and (2,-7) The equation is ___. Here's what, I did: Slope = rise/run = y2 - y1/ x2 - x1, where x2 - x1 # 0 Substitute the coordinates of the points into

You can view more similar questions or ask a new question.