Ancestral's definitions
A first order ordinary differential equation - that is, an equation that relates a function of one variable and it's first derivative in some way.
"Why Elwood, how do I find the solution to dy/dx = y/x?"
"Well that's a simple matter, Eleanor, though I know not why a woman such as yourself would have an interest in maths. That is an example of a separable first order ordinary differential equation, or separable FOODE. Rearrange to get (1/y)dy = (1/x)dx, and integrate both sides to get lny = lnx + c. You may then solve for y, yielding y = xexp(c), where c is an arbitrary constant of integration. Noting exp(c) is itself an arbitrary constant, you may simplify to y = kx. So dy/dx in that differential equation is the derivative of any straight line that passes through the origin."
"Gadzooks! It is far more elementary than I at first had imagined. Now let us get in this motor coach and ride blissfully towards the sunset."
"Well that's a simple matter, Eleanor, though I know not why a woman such as yourself would have an interest in maths. That is an example of a separable first order ordinary differential equation, or separable FOODE. Rearrange to get (1/y)dy = (1/x)dx, and integrate both sides to get lny = lnx + c. You may then solve for y, yielding y = xexp(c), where c is an arbitrary constant of integration. Noting exp(c) is itself an arbitrary constant, you may simplify to y = kx. So dy/dx in that differential equation is the derivative of any straight line that passes through the origin."
"Gadzooks! It is far more elementary than I at first had imagined. Now let us get in this motor coach and ride blissfully towards the sunset."
by Ancestral January 8, 2010
Get the foodemug.