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What are the prereqs for differential equations? Do you need to know integral calculus too, and if so, to what extent? I want to learn about DE's as quick as possible but I'm not sure if I'm ready yet, my differential calculus is up to par I believe but my integral calculus is pretty weak, is that going to be a problem?

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    Well, take Newton's laws for a start. Acceleration is the derivative of velocity, which is the derivative of the position. And the acceleration of a body is proportional to the force acting on it, which usually depends on its position, and on the positions of other bodies involved. And there you have a system of differential equations right away! (There are many many other examples too, but that's the origin of the whole subject.)2012-11-29

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When solving DEs, we can often leave the integrals in the solutions unsimplified as simplifying the integrals are not the key points when solving DEs, but it doesn't mean than we can completely ignore integral calculus when solving DEs. Because some of the DEs must involve integral calculus to solving. For example:

  1. Some of types of DEs require integration on both sides when solving, e.g. the DEs of the type http://eqworld.ipmnet.ru/en/solutions/ode/ode0328.pdf.

  2. When solving the DEs of the type $\sum\limits_{k=0}^n(a_kx+b_k)y^{(k)}(x)=0$ without any aids of known special functions, it is known that quite a lot of the cases can be solved by assuming the integral kernel of the form $y=\int_Ce^{xs}K(s)~ds$ , and some of the processes should involve differentiation under the integral sign.

So you have the freedom to completely ignore integral calculus when solving DEs, but you will become the disadvantages of solving some types of DEs.