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 in part (a) find lim F(x) X goes to infinity

  1. 👍 0
  2. 👎 0
  3. 👁 408
  1. dy/dx = (y - 1)/ x^2
    Use the integration method of separation of variables.

    dy/(y-1) = dx/x^2

    ln (y-1) = -1/x + C

    You say that the initial condition is
    f(x) = y = 0 at x =2

    Are you sure the initial condition is not f(0) = 2 ? You cannot have a logarithm of a negative number.

    1. 👍 0
    2. 👎 0
  2. Start like above, but once you gget to the logarithm part, it is in absolute values, so it is ln(1) which is 0. Solve from there

    1. 👍 0
    2. 👎 0
  3. The two statements above is wrong.

    you first move around the
    dy/dx = (y-1)/x^2 into

    dy/(y-1) = dx/x^2

    Then you integral where it turns to

    ln( (y-1)/C ) = -1/x

    Next you move the e from the ln to the other side

    (y-1)/C = e^(-1/x)

    After that you times C to both sides and move the -1 afterwords

    y-1 = Ce^(-1/x) --> y = Ce^(-1/x)+1

    I not sure how you do part (b) though.
    Sorry

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Differential Equations

    The velocity v of a freefalling skydiver is well modeled by the differential equation m*dv/dt=mg-kv^2 where m is the mass of the skydiver, g is the gravitational constant, and k is the drag coefficient determined by the position

  2. Calculus

    Suppose that we use Euler's method to approximate the solution to the differential equation 𝑑𝑦/𝑑𝑥=𝑥^4/𝑦 𝑦(0.1)=1 Let 𝑓(𝑥,𝑦)=𝑥^4/𝑦. We let 𝑥0=0.1 and 𝑦0=1 and pick a step size ℎ=0.2.

  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. Help with differential eqs problem???? (Calculus)

    Consider the differential equation dy/dt=y-t a) Determine whether the following functions are solutions to the given differential equation. y(t) = t + 1 + 2e^t y(t) = t + 1 y(t) = t + 2 b) When you weigh bananas in a scale at the

  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

    Consider the differential equation dy/dx = 2x - y. Let y = f(x) be the particular solution to the differential equation with the initial condition f(2) = 3. Does f have a relative min, relative max, or neither at x = 2? Since

  3. algebra 2 multiple choice HELP

    find f(a), if f(t) = 2t2(squared)-t-2 A. 2(a+t)2(squared)-2t+1-2 B. 2(t+a)2(squared)-2(t+a)-2 C. 2a2(squared)-a-2 D. 4a2(squared)-2a-2 I put (squared) because the two in front of it means it's being squared... please help. thanks!

  4. 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

  1. math

    Which shows a perfect square trinomial? 50 y squared minus 4 x squared 100 minus 36 x squared y squared 16 x squared + 24 x y + 9 y squared 49 x squared minus 70 x y + 10 y squared

  2. calc

    The differential equation dy dx equals the quotient of x and y squared. will have a slope field with negative slopes in quadrant I will have a slope field with positive slopes in all quadrants will produce a slope field with

  3. Differential Equations

    Consider the differential equation: dy/dt=y/t^2 a) Show that the constant function y1(t)=0 is a solution. b)Show that there are infinitely many other functions that satisfy the differential equation, that agree with this solution

  4. 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

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