variaveis separaveis

Question

resolva as equações diferenciais propostas por variaveis separaveis dy/dx x^2/y(1+x^3)

Answer 1

I assume you want to solve 

 

dy/dx = x² / [y(1 + x³)]

 

using separation of variables.

 

ydy = x²dx / (1 + x³)

 

ydy = (1/3) 3x²dx / (1 + x³)

 

Integrate both sides.

 

y²/2 + c = (1/3) ln(1 + x³)

 

You can take it from here.