Lately in my Physics C class we have been doing differential equations, which my teacher has explained more than once to me. Yet for some reason I can still not grasp the concept, I think my problem lies in not understanding the process of solving a differential equation. So my question then becomes what is the general process for solving a differential equation of the first order? I am a high school senior and a physics major by heart, so I really need to understand this process before I go to college. I am in Calculus AB and any answers are appreciated.
General Process to Solve a Differential Equation
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calculus
ordinary-differential-equations
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1In a differential equation, the unknown is a *function*, and the equation involves derivatives of the unknown. As to "the general process for solving a differential equation", there's entire courses devoted to methods. Even "first order" is not really enough, as there are several kinds of "first order" equations. Linear? Separable? – 2011-12-14
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1Unfortunately, there is no single process to solve an arbitrary first order equation. The task of finding such a method is fairly hopeless. However, at the calculus AB level, separation of variables and substitution is usually all you need. You may want to google those terms. – 2011-12-14
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1And to add to the two methods mentioned, about the only other method that might come into play is that of an integrating factor. – 2011-12-14