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

Dolly Robinson

Dolly Robinson

Answered question

2021-05-19

Establishes the order of the given Ordinary Differential Equation. Also determine if the equation is linear or not
(sin0)y(cos0)y=2

Answer & Explanation

Derrick

Derrick

Skilled2021-05-20Added 94 answers

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
(sin0)y(cos0)y=2 then
(sin0)(y(cos0)sin0y)=2
(y(cos0)sin0y)=2(sin0)
y(cot0)y=2(sin0)...(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

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