First-Order ODE Flashcards
containing at least one partial derivative of some dependent variable
Partial Differential Equation (PDE)
It does not depend on whether the function is an ordinary or partial derivatives
order of the differential equation
Variable in an equation appears only with a
degree of one
linear differential equation
Non-empty set of solutions specified by an expression which contains at least one parameter. It contains arbitrary constant C.
general solution
A solution of a differential equation over a region R is a?
set of functions
It is the largest derivative present in the differential equation
order of the differential equation
is a differential equation for a function of a single variable
Ordinary Differential Equation (ODE)
It is the exponent of the highest order derivative involved in the differential equation when the differential equation satisfies the following conditions
degree of differential equation
it is any equation which contains derivatives, either ordinary derivatives or partial derivatives
differential equation
No products of the dependent variable and/or
its derivatives are present
linear differential equation
There shouldn’t be involvement of highest order derivative as a?
transcendental function, trigonometric or exponential
The equation 𝑴 𝒙, 𝒚 𝒅𝒙 + 𝑵 𝒙, 𝒚 𝒅𝒚 = 𝟎 is an _____________________ if there exists a function f of two variables x and y having continuous partial derivatives such that the general solution of the equation is f(x,y) = C.
exact differential equation
It is a mathematical equation that relates some function with its derivatives
differential equation
No transcendental functions (sine, cosine, 𝑒𝑦 ,
arcsin, log etc.) of the dependent variables
and/or its derivatives are present
linear differential equation
Each individual solution of a differential equation. It does not contain arbitrary constant.
particular solution
