mathematics

find the general solution to the following differential equation dy/dx=-(In(x))/(x^2)*y^1/2 (x>0,(y>0)give answer in implicit form.

  1. 👍 0
  2. 👎 0
  3. 👁 177
  1. Use separation of variables. I don't know if the y^(1/2) is supposed to be in the denominator or not. Let's supposed it is not. Then

    dy/dx= -[(ln(x))/(x^2)]*y^1/2
    y(-1/2) dy = -ln(x)/x^2 dx

    Integrate both sides separately, and add a constant.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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.

  2. 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

  3. 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?

  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?

  1. 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

  2. Calculus

    Find a solution to the equation if possible. Give the answer in exact form and in decimal form. 8=4sin(5x)

  3. Calculus check my answers

    1. The general solution of the differential equation dy - 0.2x dx = 0 is a family of curves. These curves are all: a. lines b. hyperbolas c. parabolas (my answer) d. ellipses 2. The table below gives selected values for the

  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. Math (Calc) (Differential Equation Solution)

    Some of the curves corresponding to different values of C in the general solution of the differential equation are shown in the graph. Find the particular solution that passes through the point (0, 2). y(x^2+y) = C 2xy +

  2. Calculus

    Find a solution to the equation if possible. Give the answer in exact form and in decimal form. 8=4sin(5x)

  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. Calculus

    Find the solution t the differential equation dz/dt = 2te^z that passes through the origin. My answer is -In (1-t^2), but my answer is populating as incorrect. Can someone help please?

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