Ex1 d y d x = x 2 y 2 {\displaystyle {dy \over dx}={x^{2} \over y^{2}}}
y 2 ∗ d y = x 2 ∗ d x {\displaystyle y^{2}*dy=x^{2}*dx}
∫ y 2 ∗ d y = ∫ x 2 ∗ d x {\displaystyle {\int y^{2}*dy}={\int x^{2}*dx}}
∫ y 2 ∗ d y = y 3 3 {\displaystyle {\int y^{2}*dy}={y^{3} \over 3}}
∫ x 2 ∗ d x = x 3 3 {\displaystyle {\int x^{2}*dx}={x^{3} \over 3}}
But one side of the equation needs to add a constant c.
y 3 3 = x 3 3 + c {\displaystyle {y^{3} \over 3}={x^{3} \over 3}+c}
y 3 = x 3 + 3 c {\displaystyle y^{3}=x^{3}+3c}
constant times 3 will still be constant so 3c-> c.
y 3 3 . = x 3 + c 3 {\displaystyle {\sqrt[{3}]{y^{3}}}.={\sqrt[{3}]{x^{3}+c}}}
Ex2 y' = xy d y d x = x y {\displaystyle {dy \over dx}=xy}
d y = x y ∗ d x {\displaystyle dy=xy*dx}
d y y = x ∗ d x {\displaystyle {dy \over y}=x*dx}
∫ 1 y d y = ∫ x ∗ d x {\displaystyle \int {1 \over y}dy=\int x*dx}
∫ 1 y d y = l n | y | {\displaystyle \int {1 \over y}dy=ln|y|}
∫ x ∗ d x = x 2 2 + c {\displaystyle \int x*dx={x^{2} \over 2}+c}
https://www.youtube.com/watch?v=C7nuJcJriWM&list=PLEjLk3Wl8akWPgisw-u9jrmdN67dgPibe&index=33
![{\displaystyle {\sqrt[{3}]{y^{3}}}.={\sqrt[{3}]{x^{3}+c}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d814a609e3f362a5b9f11d267424e10a514ac4f9)
