How do you change the form of a differential equation from dy/dt to f(y,t)? If I have dy/dx = y/A(y) + 1 where A(y) is the area of a cross section of a conical base. How can I change A(y) to t?
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 equation of the form (water flow rate) $\displaystyle y' = -0.6*\pi*r^2\sqrt{2g}\frac{\sqrt{y}}{A(y)}$ where r = 0.1 the radius of the orifice, g = 32, y(0) = 8, initial volume = 512(pi/3), A(y) is the area of the cross section of the tank x units above the orifice, into a form f(y,t) so I can apply the Euler method.
I think A(y) is supposed to be t but I don't know how to rewrite it to become t.