question overall accuracy: 69.6% record: 11 score: 11 what would be a step in solving the differential…

question overall accuracy: 69.6% record: 11 score: 11 what would be a step in solving the differential equation dy/dx = e^(x + 2)y^3? ∫y^3dy = ∫1/e^(x + 2)dx ∫1/y^3dy = ∫e^(x + 2)dx ∫1/y^3dy = ∫1/e^(x + 2)dx ∫y^3dy = ∫e^(x + 2)dx high score board: overall refresh you must have at least 100 to be on the board. # name record 1 isabelle engel 130

question overall accuracy: 69.6% record: 11 score: 11 what would be a step in solving the differential equation dy/dx = e^(x + 2)y^3? ∫y^3dy = ∫1/e^(x + 2)dx ∫1/y^3dy = ∫e^(x + 2)dx ∫1/y^3dy = ∫1/e^(x + 2)dx ∫y^3dy = ∫e^(x + 2)dx high score board: overall refresh you must have at least 100 to be on the board. # name record 1 isabelle engel 130

Answer

Explanation:

Step1: Separate variables

For the differential equation $\frac{dy}{dx}=e^{x + 2}y^{3}$, we can rewrite it in the form of separating variables. Move the terms involving $y$ to one - side and the terms involving $x$ to the other side. Divide both sides by $y^{3}$ (assuming $y\neq0$) and multiply both sides by $dx$. We get $\frac{1}{y^{3}}dy=e^{x + 2}dx$.

Answer:

$\int\frac{1}{y^{3}}dy=\int e^{x + 2}dx$