Equation of Curve Passing Through (0, 9)

  • Thread starter Thread starter locachola17
  • Start date Start date
  • Tags Tags
    Curve
locachola17
Messages
6
Reaction score
0

Homework Statement



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?

Homework Equations





The Attempt at a Solution



im thinking the slope would then be 18...but i haven't gotten much farther than that
 
Physics news on Phys.org
Keep in mind that derivative equals slope at a given point.
 
EstimatedEyes said:
Keep in mind that derivative equals slope at a given point.

Right. And slope=derivative. So you want to solve the differential equation y'(x)=2*y(x).
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Equation of a Curve Passing Through (0, 9)
Replies
12
Views
4K
Simmons 7.10 & 7.11: Find Curves Intersecting at Angle pi/4
Replies
1
Views
2K
Calculating Area Under a Curve Using Change of Variables and Quotient Rule
Replies
5
Views
2K
Finding integral curves of a vector field
Replies
3
Views
2K
Write the tangent lines to the curve
Replies
1
Views
1K
Calculating the Tangent to a Parametric Curve at a Given Point
Replies
3
Views
2K
Finding the parametric equation of a curve
Replies
2
Views
2K
Finding the equation of a curve
Replies
14
Views
2K
Find the equation of a tangent line to y = x^2?
Replies
11
Views
4K
Slope of tangent line to curves cut from surface
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top