Recent content by coolxal

To apply the Euler method, I'm given an equation of the form y' = y - t^2 + 1, 0 <= t <=2, y(0) = 0.5 and f(y,t) = y'. I set h = (b-a)/N where N is the number of iterations and h is the step size. t = a, w = y(0) then I loop w = w + h*f(t,w), t = a + i*h N times. I'm trying to change an...

How do you change the form of a differential equation from dy/dt to f(y,t)? So if I had dy/dx = y/A(y) + 1 where A(y) is the area of a cross section of a conical base.

I used the formula V = (1/3)*B*h where B = A(x) the area and h = x the height so shouldn't A(x) = (512*(pi/3))/(x/3)? So if r(x) = \frac{r(8)}{8} x and substitute it for r in V(x) = \frac{\pi}{3} r^2 x it's V(x) = \frac{\pi}{3} (\frac{r(8)}{8} x)^2 x V(8) = \frac{\pi}{3}...

V = (1/3)*A(x)*x A(x) = (512*(pi/3))/(x/3) Is that right?

Homework Statement Water flows from a conical tank with circular orifice at the rate \frac{dx}{dt} = -0.6*\pi*r^2\sqrt{2g}\frac{\sqrt{x}}{A(x)} r is the radius of the orifice, x is the height of the liquid from the vertex of cone, A(x) is area of the cross section of the tank x units above...