Differential Equations background

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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Yes. Computing $\int f(x) \, dx$ is the same as solving the differential equation $u'(x)=f(x)$, and with more complicated differential equations it only gets worse... – Hans Lundmark Nov 29 '12 at 14:50
Would being able to solve (in)definite integrals be enough? – JohnPhteven Nov 29 '12 at 15:02
For some things, yes. The first thing one learns about differential equations is usually how to solve some particular types exactly, and in those cases it mostly boils down to computing some integral. But it's a huge subject, so I guess it depends on what you're going to study. – Hans Lundmark Nov 29 '12 at 15:38
@HansLundmark For physics purposes. I am still baffled as to why differential equations play such a huge part in physics.. – JohnPhteven Nov 29 '12 at 15:39
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.) – Hans Lundmark Nov 29 '12 at 16:00

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.