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**Web Bonus Problems / Re: Web Bonus Problem –– Week 1**

« **on:**January 06, 2018, 10:23:04 AM »

$$\text{ something wrong }.$$

Hence upon substitution,

$$\text{ some other thing wrong}. $$

Thus I have the unknown functions. I think the constants and explicit forms shows up as a result of not presume these functions beforehand.

I hope what follows is no longer nonsense. We indeed have the not-so-arbitrary functions as desired,

$$c_{1}xy, c_{3}x, c_{2}y, c_{4}.$$

They lost their arbitrariness in form by constrain $(2)$, since upon substitution

$$x f_{y}(y) + g_{y}(y)=h(x)$$

the particular form of $f,g$ is dictated to be polynomial in $y$ of degree less than one.