Find the order and degree (if any) of each of the differential equations given `{:((i)(dy)/(dx)-tanx=0,(ii)((dy)/(dx))^(2)+y=e^(x)),((iii)(d^(2)y)/(dx^2)=sin3x+cos3x,(iv)(y'')^(2)+cosy'=0),((v)y+2y'+siny=0,(vi)(d^(4)y)/(dx^(4))+sin ((d^(3)y)/(dx^(3)))=0),((vii)y''+y^(2)+e^(y')=0,(viii)3(d^(2)y)/(dx^(2))+5((dy)/(dx))^(2)=log x):}`

Explanation

To find the order and degree of each of the given differential equations, we will analyze each equation step by step.

### Step-by-Step Solution:

1. **Equation (i)**: \(\frac{dy}{dx} - \tan x = 0\)
- **Order**: The highest derivative is \(\frac{dy}{dx}\), which is the first derivative. Therefore, the order is **1**.
- **Degree**: The power of the highest order derivative \(\frac{dy}{dx}\) is 1. Therefore, the degree is **1**.

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