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. 👁
  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
  3. 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. 👎
  4. Do not panic. Plug and chug.

    1. 👍
    2. 👎
  5. I think the whole non panicing ship sailed a long time ago haha. Sorry and thanks for the help!

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  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. 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

  3. 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

  4. 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

  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. Calculus

    The differential equation dy/dx = x/y^2 Possible answers: I. will have a slope field with negative slopes in quadrant I II. will have a slope field with positive slopes in all quadrants III.will produce a slope field with columns

  3. Calculus

    For Questions 1–3, use the differential equation given by dx equals xy/3, y > 0. Complete the table of values x −1 −1 −1 0 0 0 1 1 1 y 1 2 3 1 2 3 1 2 3 dy/dx ? ? ? ? ? ? ? ? ? Find the particular solution y = f(x) to the

  4. AP Calculus Help Five Questions

    1. Find the particular solution to y " = 2sin(x) given the general solution y = -2sin(x) + Ax + B and the initial conditions y(pi/2) = 0 and y'(pi/2) = -2. 2. What function is a solution to the differential equation y ' - y = 0?

  1. Calculus

    1. The differential equation dy/dx equals x-2/y-2 I .produces a slope field with horizontal tangents at y = 2 II. produces a slope field with vertical tangents at y = 2 III. produces a slope field with columns of parallel segments

  2. Calculus

    The differential equation dy/dx= -x/y I. will have a slope field with negative slopes in all quadrants II. will have a slope field with positive slopes in all quadrants III. will produce a slope field with rows of parallel

  3. Calculus

    For Questions 1–2, use the differential equation given by dy/dx = xy/3, y > 0. 1. Complete the table of values x -1 -1 -1 0 0 0 1 1 1 y 1 2 3 1 2 3 1 2 3 dy/dx 2. Find the particular solution y = f(x) to the given differential

  4. Calculus

    A differential equation that is a function of x only a.will produce a slope field with parallel tangents along the diagonal b.will produce a slope field that does not have rows or columns of parallel tangents c.will produce a

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