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 professor for help.

  1. 👍
  2. 👎
  3. 👁
  1. To find out if your answer is correct, differentiate it and see if you get the original back.
    y = x^3
    dy/dx = 3 x^2
    now put that in d dy/dx - 3 y
    x(3 x^2)- 3 x^3 = ?
    3 x^3 - 3 x^3 = 0
    sure enough it works

    1. 👍
    2. 👎
  2. Well, here try getting all the y stuff on one side and all the x stuff on the other side (separating variables)
    x dy/dx = 3 y
    dy/y = 3 dx/x
    integrate both sides
    ln y = 3 ln x
    but 3 ln x = ln x^3
    so
    ln y = ln x^3
    so
    y = x^3 will work.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Differential Equation

    What is the solution of the differential equation of (6x+1)y^2 dy/dx + 3x^2 +2y^3=0?

  2. 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

  3. Calculus

    Suppose that we use Euler's method to approximate the solution to the differential equation 𝑑𝑦/𝑑π‘₯=π‘₯^4/𝑦 𝑦(0.1)=1 Let 𝑓(π‘₯,𝑦)=π‘₯^4/𝑦. We let π‘₯0=0.1 and 𝑦0=1 and pick a step size β„Ž=0.2.

  4. 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. 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. 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 βˆ†x = 0.5?

  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

    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

  2. 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

  3. Calculus

    Which of the following is a separable, first-order differential equation? A) dy/dx= x+y/2x B) dy/dx=x+y/x-y C) dy/dx=sinx

  4. 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= ______

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