Find the order and degree of the following differential equations. i) `(dy)/(dx)+y=1/((dy)/(dx))`, ii) `e^(e^(3)y)/(dx^(3))-x(d^(2)y)/(dx^(2))+y=0` , iii) `sin^(-1)(dy)/(dx)=x+y`, iv) `log_(e)(dy)/(dx)=ax+by`
v) `y(d^(2)y)/(dx^(2))+x((dy)/(dx))^(2)-4y(dy)/(dx)=0`

Explanation

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

### i) \( \frac{dy}{dx} + y = \frac{1}{\frac{dy}{dx}} \)

1. **Rearranging the equation**: Multiply both sides by \( \frac{dy}{dx} \):
\[ \left(\frac{dy}{dx}\right)^2 + y \frac{dy}{dx} = 1 \]
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