How do you find the number of arbitrary constant in a differential equation?

Here the order of the differential equation is 2. ∴Number of arbitrary constants in the general solution of any differential equation = order of differential equation = 2 , where n is the order of the differential equation. And the number of arbitrary constants in the particular solution of a differential equation =0.

What is the number of arbitrary constant in the particular solution of differential equation of third order?

In the particular solution of a differential equation of third order, there is no arbitrary constant because in the particular solution of any differential equation, we remove all the arbitrary constant by substituting some particular values.

How do you find a particular solution to a non-homogeneous differential equation?

The general solution of a nonhomogeneous equation is the sum of the general solution y0(x) of the related homogeneous equation and a particular solution y1(x) of the nonhomogeneous equation: y(x)=y0(x)+y1(x). Below we consider two methods of constructing the general solution of a nonhomogeneous differential equation.

What does it mean to find the particular solution?

: the solution of a differential equation obtained by assigning particular values to the arbitrary constants in the general solution.

What is the initial value in an equation?

The initial value, or y-intercept, is the output value when the input of a linear function is zero. It is the y-value of the point where the line crosses the y-axis. An increasing linear function results in a graph that slants upward from left to right and has a positive slope.

What do you mean by initial condition?

An initial condition is a “starting point” for a differential equation. That is, it gives a coordinate (x,y) that satisfies the general solution to the differential equation, thus allowing one to find the value of the generic constant C. That means (x,y)⇒(1,1) satisfies the solution of the differential equation.