Determine the order and degree of each of the following differential equation. State also whether they are linear or non-linear: `y=p x+sqrt(a^2p^2+b^2),\ w h e r e\ p=(dy)/(dx)`

Explanation

We have given that

`y=p x+sqrt(a^2p^2+b^2),\ w h e r e\ p=(dy)/(dx)`,

First of all, we will rearrange the above equation as follows


`y-x frac{d y}{d x}=a sqrt{frac{b^{2}}{a^{2}}+(frac{d y}{d x})^{2}}`


here we have substituted the value of p and taken `a^{2}` out from the root

Since the above equation has rational powers we need to remove them so squaring on both sides.

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