First order differential equations Flashcards
What does a first order differential equation contain and what does a second order contain?
It contains a term which is like dx/dt to the power of one.Second order creates a term which is squared such as d^2y/dx^2.
What is differentiation with respect to time usually written as?
Depending on the order x dot or y double dot.
How can dy/dx be respresented?
With ydash or f double dash of x.
What does the number of constants found in solving a differential euqation depend on?
It depends on the order of the equation,if the order is two there will be 2 constants and etc.
What is a general solution to a differential equation?
It is a solution containing a number of constants equal to the order of the equation.Without solving exactly for those constants.
What is the particular solution of a differential equation?
It is the solution to a differential equation when information has been used to find the value of c.Eg when x=1, y=2.
What information allows you to solve the diffrential equation?
The condition is either called the intial condition or boundary condition.
What is verification?
It is a process of substituting a solution into the differential equation to verify if its legit.
What is a linear differential equation?
This is where the variable y is to the power of 1.
What form can you write non separable differential equations in?
in the form dy/dx+p(x)y=q(x)
What is the integrating factor?
It is a value that you multiply the equation with to put it into perfect derivative format.This applies for only first order linear differential equations.
How do you calculate the integrating factor?What happens to the c.
by doing e^integral of p dx.You can neglect the c.
What are 3 important things about the auxiliary equation?
No integration
Number of terms in complementary function equals order of equation
Number of unknowns in solution equals order.
What is the general solution for a second order homogenous equation with 2 distinct roots?
Ae^lambdax+Be^lambdax.This is also the complementary function.
Difference between an intial condition and a boundary condition?
Initial condition is condition given for the same value of the independent variable x.Boundary is given for different values of x.Boundary condition the solution usually lies within the boundary.
