Dolly Robinson

2021-05-19

Establishes the order of the given Ordinary Differential Equation. Also determine if the equation is linear or not
$\left(\mathrm{sin}0\right){y}^{‴}-\left(\mathrm{cos}0\right){y}^{\prime }=2$

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
$\left(\mathrm{sin}0\right){y}^{‴}-\left(\mathrm{cos}0\right){y}^{\prime }=2$ then
$⇒\left(\mathrm{sin}0\right)\left({y}^{‴}-\frac{\left(\mathrm{cos}0\right)}{\mathrm{sin}0}{y}^{\prime }\right)=2$
$⇒\left({y}^{‴}-\frac{\left(\mathrm{cos}0\right)}{\mathrm{sin}0}{y}^{\prime }\right)=\frac{2}{\left(\mathrm{sin}0\right)}$
$⇒{y}^{‴}-\left(\mathrm{cot}0\right){y}^{\prime }=\frac{2}{\left(\mathrm{sin}0\right)}$...(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