Test 1

Created by diffeq2012 

Upgrade to
remove ads

Equilibrium Solution


Stable Equilibrium

Solutions converge to it

Unstable Equilibrium

Solutions diverge from it

Semistable Equilibrium

Solutions converge to it on one side, diverge from it on the other side.

Source (repeller)

Unstable equilibrium on phase line

Sink (attractor)

Stable equilibrium on phase line


Semistable equilibrium on phase line

Needs Euler method

n, h, starting point, y'

Times in Euler's method

t0= starting t
t1=t0+h etc.

y in Euler's method

y0= strting y
y1=y0+h*y'(at starting point)

Runge Kutta 2nd order

k1= same slope as in Euler
k2= slope at point
(t0+(h/2),y value on first tangent line at half step)

Order of DE

Highest derivative

Linear DE

y,y',y'', etc all on first power. (t can be not linear)

Homogeneous DE

The term without any y is 0.

Constant coefficient DE

In front of the ys we have numbers

Variable coefficient DE

There is a y with not a number in front of it.

Separable DE

can be written as

Integrating Factor

Integrating factor: e^(integral p(t) dt)
Only for linear, first order DE!

Superposition for HOMOGENEOUS

If y1 and y2 are solutions then
cy1+ky2 is also a solution

Non-homogeneous principal

yh is the general solution to the associated homogeneous DE.
yp is a particular solution to the non-homog. DE.

Solution to


Exponential growth or decay equation


Solution to y'=ky


Mixing Problem

x= amount of salt present
(dx)/(dt)=rate in-rate out
rate in=(flow rate in)*(concentration in)

Newton's Law of Cooling

T= temperature of object, M constant temp.

Logistic Equation

(dy)/(dt)= (r-ay)y = ry-ay^2
Limit L=r/a

Please allow access to your computer’s microphone to use Voice Recording.

Having trouble? Click here for help.

We can’t access your microphone!

Click the icon above to update your browser permissions above and try again


Reload the page to try again!


Press Cmd-0 to reset your zoom

Press Ctrl-0 to reset your zoom

It looks like your browser might be zoomed in or out. Your browser needs to be zoomed to a normal size to record audio.

Please upgrade Flash or install Chrome
to use Voice Recording.

For more help, see our troubleshooting page.

Your microphone is muted

For help fixing this issue, see this FAQ.

Star this term

You can study starred terms together

NEW! Voice Recording

Create Set