# Equation of a curve

1. Mar 17, 2009

### locachola17

1. The problem statement, all variables and given/known data

A curve passes through the point (0, 9) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve?

2. Relevant equations

3. The attempt at a solution

2. Mar 17, 2009

### gabbagabbahey

Hi locachola, welcome to PF!

We're not here to do your homework for you, we're here to help you learn. You must show some attempt at a solution, in order to receive help....

3. Mar 17, 2009

### lanedance

Hi locachola17 wlecome to PF

The idea of the forum is to help with your working... so any ideas on how to get started?

as a hint, the line
"has the property that the slope of the curve at every point P is twice the y-coordinate of P"
can you write this line as an equation?

4. Mar 17, 2009

### locachola17

okay well at the point (0,9) the y-coordinate is 9
if the slope is twice the y-coordinate, the slope is 18?!

5. Mar 17, 2009

### gabbagabbahey

Sure, but what about at any other point (x,y) on the curve? What does that tell you about dy/dx for this curve?

6. Mar 17, 2009

### lanedance

thats for that single point....

but the question says its true for every point on the line... how would you write this to show it for every point on the line...?

remeber the slope is given by the derivative y'(x) = dy/dx

7. Mar 17, 2009

### locachola17

dy/dx is 2y

8. Mar 17, 2009

### gabbagabbahey

Right, so y(x)=____?

9. Mar 17, 2009

### gabbagabbahey

No it doesn't...It says for every point on the "curve"....the curve is not a line

10. Mar 17, 2009

### locachola17

y(x)=y^2

11. Mar 17, 2009

### gabbagabbahey

That makes no sense, you have a separable differential equation for y(x): $$\frac{dy(x)}{dx}=2y(x)$$....how do you usually solve a separable DE?

12. Mar 17, 2009

### locachola17

you integrate both sides?

13. Mar 17, 2009

### gabbagabbahey

How do you determine $$\int y(x)dx$$ when you don't know what y(x) is?

No, you separate varaiables first and then integrate:

$$\frac{dy}{dx}=2y\implies \frac{dy}{y}=2dx$$

Now you can integrate....