Establishes the order of the given Ordinary Differential Equation. Also determine if the equation is...

Step 1
Order:- The order of a differential equation is, the highest -order derivative of equation.
Linearity:- A differential equation is called linear if dependent variable and its derivatives have degree 1.
Step 2
Given differential equation is
$(\sin 0)y^{‴}-(\cos 0)y^{\prime }=2$ then
$\Rightarrow (\sin 0)(y^{‴}-\frac{(\cos 0)}{\sin 0}{y}^{\prime })=2$
$\Rightarrow (y^{‴}-\frac{(\cos 0)}{\sin 0}{y}^{\prime })=\frac{2}{(\sin 0)}$
$\Rightarrow y^{‴}-(\cot 0)y^{\prime }=\frac{2}{(\sin 0)}$...(1)
Here, in given equation highest order derivative is y'''
So, order of differential equation = 3.
Since, in equation (1), we can see dependent variable and its derivative have degree 1 so, given differential equation is linear.
Step 3
Answer:
Order: 3
given differential equation is linear