Talk:Ordinary Differential Equations/Structure of Differential Equations

This text keeps referring to d/dx as the gradient of f(x). That's not correct. The derivative of a function at a given point is the slope of a line tangent to that point. The gradient is orthogonal to the tangent line. Can anyone back me up on this? Instead of saying gradient, this page should say tangent.

The task is said often to be to "solve" the DE. This was always confusing to me when I studied this. Up to this point most people studying DEs would be familiar with "solve" meaning to get a numerical answer. Should this be restated as rewriting the equation so that Y (the independant variable) is in terms of only functions of X (the independent variable)? Or maybe, solving for Y? ____________________________________________

The section 'Solutions of a Differential Equation' ends with 'This is easily solvable with the following theorem that you probably have already proved in Calculus:'. Cliffhangers do not belong in technical books ! TomG (discuss • contribs) 01:46, 16 July 2012 (UTC)