Determine the order and degree of each of the following differential equation. State also whether they are linear or non-linear: `(x y^2+x)dx+(y-x^2y)dy=0`

Explanation

We have given

`(x y^2+x)dx+(y-x^2y)dy=0`


The above equation can be written as

`x(y^{2}+1) d x=y(x^{2}-1) d y `

`frac{d y}{d x}(x^{2}-1) y=x(y^{2}+1) `

`frac{d y}{d x} x^{2} y-frac{d y}{d x} y=x y^{2}+x`

So, from this equation it is clear that order of the differential equation is `1 `and the degree of the differential equation is also `1` .

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