Diff eq Definition and 264 Threads

When you are trying to determine the general solution of a homogeneous linear ordinary differential equation, after you find the roots, how do you decide which goes with c1 and which goes with c2? example: y''-3y'+2y=0 Factoring the auxiliary equation m^2-3m+2=0=(m-1)(m-2) is...

I'm hacking at this particular linear system: dY/dt = [1, -1; 1, 3] Y I've already found myself a solution using the following function: Y(t) = [ te^(2t), -(t+1)e^(2t) ] That was fun, actually, once I figured out what the hell I was doing. Here's my question: the next part of...

Ok, I was given: Solve the following using superposition: \ddot{x}+2\dot{x}+4x=\delta(t) bounded by \dot{x}=0, x(0)=0 I solved the Homo eqn and got the following: x(t)=e^{-t}(\cos (\sqrt{3}t)+\frac{\sqrt{3}}{3}\sin ({\sqrt{3}t)) I also know that : \ddot{x}+2\dot{x}+4x=u(t)...

The book only has one example of this and it's really confusing me. (x^2+y^2)dx+(x^2-xy)dy=0 I can see that it's homogeneous of degree 2 They then let y = ux From there they state that dy = udx+xdu (I'm not sure where this is coming from, but can just accept it on faith if I have to)...

I'm pretty sure I know the answer to this, just want to double check. For the problems that I'm currently working on, we are just solving the problems for an unknown constant C. I just finished one were I came up with \frac{x^2}{2}-y^2cos x-xy^3=C The book shows the solution as...

dv(t)/dt + 200v(t) = 10 cos(100t) v(0)=0 find v(t) i know v(t) is going to have an exponential and sinusoid component i also know that 200*ke^-st=-ske^-st so, s = -200. i don't know how to find k. i also can't figure out how the sinusoid part is going to be. the equations from my...

I am considering taking 1 or the other and possibly both next semester. Is there any advantage to taking one of them first, will taking calc III help me with diff eq or vice versa?

Can somone recommend a good diff EQ book? Something that would be good for learning it on your own. I'm majoring in electrical engineering, not mathmatics, if that makes any difference to your suggestions. Thanks.

x(dy/dx) = y*e^(x/y) - x its either separable, linear, homogeneous, bernoulli or exact. only thing i can figure is that its linear. how do i break it down to figure it out? the e^x/y is what's throwing me off.

Suppose the population of mosquitos in a certain area increases at a rate proportional to the current population... in the absense of other factors, the population doubles each week. There are 200,000 mosquitos in the area initially, and predators (birds, etc) eat 20,000 mosquitos /day...

Please solve r=Kt/((dr/dt)2-c2) where r and t are variables, and K and c are constants.

Nonhomogeneous system of lineair differential equations This is a given system: D\vec{y} = A\vec{y} + \vec{b} With A=\left\begin{array}{ccc}1&1&1\\0&2&1\\0&0&3\end{array}\right And \vec{b}=\left\begin{array}{c}e^4^t\\0\\0\end{array}\right We find \vec{y}_H = Y(t) \cdot \vec{c} With...

What is the true use of Differential Equations?

Check my math! I've derived a differential equation for strings starting from Stokes Theorems to show that energy is conserved along the world-sheet. These diff eq's involve connection coefficients. And I'm not really sure what it all meants yet. I would appreciate it if some who are more...