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

Answer:

Order: 3

given differential equation is linear

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

Answer:

Order: 3

given differential equation is linear