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

  1. 👍
  2. 👎
  3. 👁
  1. dy/dx = -2x/y
    y dy = -2x dx
    1/2 y^2 = -x^2 + C
    since y(1) = 1
    -1+C = 1/2
    C = 3/2

    y^2 = -2x^2 + 3

    1. 👍
    2. 👎
    👤
    oobleck

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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

  2. calculus

    is y = x^3 a solution to the differential equation xy'-3y=0?? how do i go about solving this??? also, is there a trick to understanding differential equations? i'm really struggling with this idea, but i'm too embarassed to ask my

  3. Calc 2

    Find the solution of the differential equation that satisfies the given initial condition. dy/dx= x/y, y(0) = −7

  4. 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

  1. Calculus

    Using separation of variables, solve the following differential equation with initial conditions dy/dx = e^(2x+3y) and y(0) = 1. Hint: use a property of exponentials to rewrite the differential equation so it can be separated

  2. Calculus

    Find the specific solution of the differential equation dy/dx= 4y/x^2 with condition y(-4) = e.

  3. 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

  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. math

    Can someone please help? Solve the differential equation dy/dx = 6xy with the condition y(0) = 40 Find the solution to the equation y= ______

  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

    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. 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.

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