# Establishes the order of the given Ordinary Differential Equation. Also determine if the equation is linear or not (\sin 0)y'''-(\cos 0)y'=2

Establishes the order of the given Ordinary Differential Equation. Also determine if the equation is linear or not
$$(\sin 0)y'''-(\cos 0)y'=2$$

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Derrick
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
$$(\sin 0)y'''-(\cos 0)y'=2$$ then
$$\Rightarrow (\sin 0)(y'''-\frac{(\cos 0)}{\sin 0}y')=2$$
$$\Rightarrow (y'''-\frac{(\cos 0)}{\sin 0}y')=\frac{2}{(\sin 0)}$$
$$\Rightarrow y'''-(\cot 0)y'=\frac{2}{(\sin 0)}$$...(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
Order: 3
given differential equation is linear