Busy. Please wait.

Forgot Password?

Don't have an account?  Sign up 

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.

By signing up, I agree to StudyStack's Terms of Service and Privacy Policy.

Already a StudyStack user? Log In

Reset Password
Enter the email address associated with your account, and we'll email you a link to reset your password.

Remove ads
Don't know (0)
Know (0)
remaining cards (0)
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

Diff Eq

definitions for differential equations terms

IVP A differential equation with initial values is called an initial value problem: y(x_0)=c_0,y'(x_0)=c_1,...,y^(n-1)(x_0)=c_(n-1)
Homogeneous Equation If f(&x,&y)=&^kf(x,y), then f is said to be homogeneous of degree k, where k is a real number.
differential equation An equation that contains derivatives of differentials of one or more variables is said to be a differential equation.
dependent variable A dependent variable is a function of an independent variable (allowed to vary on its own).
parameters Parameters are quantities allowed to vary beside the variables, but are not either independent or dependent.
order of diff eq The order of a differential equation is the order of the highest-ordered derivative in the equation (not the degree).
general form of nth order diff eq F(x,y,dy/dx,d2y/dx2,...,dny/dxn)=0
solution of diff eq y_1 is a solution of F(x,y,...,dny/dxn)=0 if: (a) y_1 is n-times differentiable (b) F(x,y_1,...,dny_1/dxn)=0
explicit solution A solution in explicit form is called an explicit solution (the dependent variable is written explicitly as a functioin of the independent variable(s) only).
implicit solution g(x,y)=0 is an implicit solution if it defines at least one real explicit solution to the differential equation on a given interval
particular solution A particular solution is a solution without any arbitrary constants; these arbitrary constants are plugged in for.
general solution A general solution is a solution form which every solution can be derived (by choosing arbitrary constants).
singular solution A solution that cannot be obtained by giving values to arbitrary constants in a family of solutions is called a singular solution
autonomous equation y'=f(y) where f, the driving function, is a function of the dependent variable only is called an autonomous equation. The independent variable does not appear explicitly.
Created by: efgray