Solve Differential Equation by means of Separating Variables

Examples

Ex1 ${dx \over dy}={x^{2} \over y^{2}}$

$y^{2}*dy=x^{2}*dx$

${\int y^{2}*dy}={\int x^{2}*dx}$

${\int y^{2}*dy}={y^{3} \over 3}$

${\int x^{2}*dx}={x^{3} \over 3}$

But one side of the equation needs to add a constant c.

${y^{3} \over 3}={x^{3} \over 3}+c$

$y^{3}=x^{3}+3c$

constant times 3 will still be constant so 3c-> c.

${\sqrt[{3}]{y^{3}}}.={\sqrt[{3}]{x^{3}+c}}$