Dolly Robinson

2021-05-19

Establishes the order of the given Ordinary Differential Equation. Also determine if the equation is linear or not

$(\mathrm{sin}0){y}^{\u2034}-(\mathrm{cos}0){y}^{\prime}=2$

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

$(\mathrm{sin}0){y}^{\u2034}-(\mathrm{cos}0){y}^{\prime}=2$ then

$\Rightarrow (\mathrm{sin}0)({y}^{\u2034}-\frac{(\mathrm{cos}0)}{\mathrm{sin}0}{y}^{\prime})=2$

$\Rightarrow ({y}^{\u2034}-\frac{(\mathrm{cos}0)}{\mathrm{sin}0}{y}^{\prime})=\frac{2}{(\mathrm{sin}0)}$

$\Rightarrow {y}^{\u2034}-(\mathrm{cot}0){y}^{\prime}=\frac{2}{(\mathrm{sin}0)}$ ...(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

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