In some math model tutorial faced with such cosequence of statements. Can't remember how to find simplification in math diff equations. Could someone help, how the second statement has been simplified to the third? Why we could consider dx and dy as const?
This step is done by integrating (this is usually what we do when we separate the $\mathrm dx$ and $\mathrm dy$ as shown).$$ax\,\mathrm dx=by\,\mathrm dy\implies \int ax\,\mathrm dx=\int by\,\mathrm dy\\\implies \frac12a x^2+C_1=\frac12by^2+C_2\\\implies ax^2-by^2=2(C_2-C_1)=\text{constant}$$