Busy. Please wait.

show password
Forgot Password?

Don't have an account?  Sign up 

Username is available taken
show password


Make sure to remember your password. If you forget it there is no way for StudyStack to send you a reset link. You would need to create a new account.
We do not share your email address with others. It is only used to allow you to reset your password. For details read our Privacy Policy and Terms of Service.

Already a StudyStack user? Log In

Reset Password
Enter the associated with your account, and we'll email you a link to reset your password.
Don't know
remaining cards
To flip the current card, click it or press the Spacebar key.  To move the current card to one of the three colored boxes, click on the box.  You may also press the UP ARROW key to move the card to the "Know" box, the DOWN ARROW key to move the card to the "Don't know" box, or the RIGHT ARROW key to move the card to the Remaining box.  You may also click on the card displayed in any of the three boxes to bring that card back to the center.

Pass complete!

"Know" box contains:
Time elapsed:
restart all cards
Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.

  Normal Size     Small Size show me how

Math 312 test 1

different terms revolving around differential equations

ordinary differential equations equations involving a function and its derivatives
order the order of the highest derivative
general solution y=mt+b since we don't know the values for m and b
particular solution a solution with a specific value for c, from an initial value problem
interval of existence a set of t-values for which the solution x(t) is defined
existence and uniqueness theorem if f(t,x) and its derivative are continuous near x0 and t0 then the IVP has one and only one solution
autonomous if the RHSde has no explicit t's
homogeneous if q(t)=0 in an ode
linear ode formula dx/dt=p(t)*x+ q(t)
integrating factor used to write the LHS as the derivative of the product of itself and the dependent variable x
law of cooling dx/dt= a(x(t)-b) and soln: x(t)=b+(x0-b)*e^(-at)
exponential decay dx/dt=-r*x and soln: x(t)=x0*e^(-rt)
exponential growth dx/dt=-r*x and soln: x(t)=x0*e^(rt)
general form for nonhomogeneous ode x=xh+xp assuming p is constant
critical point/equilibrium in an autonomous ode set dx/dt=0 to find this
3 types of equilibriaugh sink, source, shunt
sink if f is decreasing through xe, also if f'(xe)<0
source if f is increasing through xe, also if f'(xe)>0
shunt if f has a local min or max at xe
nonhyperbolic equilibrium if f'(xe)=0
hyperbolic equilibrium if f'(xe)does not =0, this is easier to determine behavior from
linearization way of studying solutions of nonlinear x'=f(x) near a hyperbolic equilibrium xe
separation of variables can be used for all autonomous and some nonautonomous odes if x'=f(t,x) can be separated to f(t,x)=g(t)*h(x)
Created by: lfalkens