1.E 2.O 3.A 4.D 5.Y 6. N 7.E 8. A 9.O 10.V here's half
Answer:
Option A
Step-by-step explanation:
Given differential equtaion is ![y+\left ( \frac{\mathrm{d} y}{\mathrm{d} x} \right )^2=C](https://tex.z-dn.net/?f=y%2B%5Cleft%20%28%20%5Cfrac%7B%5Cmathrm%7Bd%7D%20y%7D%7B%5Cmathrm%7Bd%7D%20x%7D%20%5Cright%20%29%5E2%3DC)
As this equation contains derivatives and not partial derivatives, this equation is an ordinary differential equation and not a partial differential equation.
Here,
denotes that x is an independent variable and y is a dependent variable.
Order of the differential equation is a number of the highest derivative.
Order of the given differential equation is 1.
We can write this ordinary differential equation as follows:
![y+\left ( \frac{\mathrm{d} y}{\mathrm{d} x} \right )^2=C\\\left ( \frac{\mathrm{d} y}{\mathrm{d} x} \right )^2=C-y\\\frac{\mathrm{d} y}{\mathrm{d} x}=\sqrt{C-y}](https://tex.z-dn.net/?f=y%2B%5Cleft%20%28%20%5Cfrac%7B%5Cmathrm%7Bd%7D%20y%7D%7B%5Cmathrm%7Bd%7D%20x%7D%20%5Cright%20%29%5E2%3DC%5C%5C%5Cleft%20%28%20%5Cfrac%7B%5Cmathrm%7Bd%7D%20y%7D%7B%5Cmathrm%7Bd%7D%20x%7D%20%5Cright%20%29%5E2%3DC-y%5C%5C%5Cfrac%7B%5Cmathrm%7Bd%7D%20y%7D%7B%5Cmathrm%7Bd%7D%20x%7D%3D%5Csqrt%7BC-y%7D)
As this equation is of form
, this is a linear differential equation.
So, option A. is correct as this is a linear ordinary differential equation.
Answer: Yeah its a rational number.