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.