# 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. 👎

## 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/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.

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 ∆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= ______