dm84z28 said:
Hello alll. i am enrolled in Differential Equation Calc this semester. i was wondering what kind of stuff will i be doing and what should i expect in terms of difficulty etc. thanks in advance
I assume you've had basic algebra so you should be familiar with classical equation in 1 or more variables. I also assume that you've had basic calculus, derivatives and integrals. With differential equations, these two fundamental concepts of calculus meet each other. In these equations, the unknown is no longer just 'x' (or more variables) but a function y and its derivatives (y', y'', ...).
You'll be studying (and trying to solve, i.e. integrate) equations which involves derivatives. For example, if y is a function of x, consider one of the most basic DE (differential equations): y' = y. Of course, as you probably know, the exponential function e^x is its own derivative, so a solution of this DE will be y = e^x. Notice that we still have a solution if we multiply this solution with a constant, so the general solution will be y = ce^x.
Now we just 'guessed' the answer, but how could we really find it without guessing? Well you know that y' means the derivative of y with respect to x, y' is nothing more than dy/dx. Solving yields:
y' = y \Leftrightarrow \frac{{dy}}<br />
{{dx}} = y \Leftrightarrow \frac{{dy}}<br />
{y} = dx \Leftrightarrow \int {\frac{{dy}}<br />
{y}} = \int {dx} \Leftrightarrow \ln \left| y \right| = x + C \Leftrightarrow e^{\ln \left| y \right|} = e^{x + C} \Leftrightarrow y = ce^x
Now it's also clear why I called 'solving the DE' also 'integrating the DE' and where the connection with integrals lies. It's also easy to see where this constant came from, note that e^C is just another constant which I named c.
Well this was very basic but I hope now you get the idea about differential equations, we're trying to find a function which satisfies the differential equation for all x
Good luck!
