overall accuracy: 84% record: 17 score: 17 what would be a step in solving the differential equation dy/dx =…

overall accuracy: 84% record: 17 score: 17 what would be a step in solving the differential equation dy/dx = e^(x - 2)y^2? ∫1/y^2dy = ∫e^(x - 2)dx ∫y^2dy = ∫1/e^(x - 2)dx ∫1/y^2dy = ∫1/e^(x - 2)dx ∫y^2dy = ∫e^(x - 2)dx high score board: overall you must have at least 100 to be on the board. # name record

overall accuracy: 84% record: 17 score: 17 what would be a step in solving the differential equation dy/dx = e^(x - 2)y^2? ∫1/y^2dy = ∫e^(x - 2)dx ∫y^2dy = ∫1/e^(x - 2)dx ∫1/y^2dy = ∫1/e^(x - 2)dx ∫y^2dy = ∫e^(x - 2)dx high score board: overall you must have at least 100 to be on the board. # name record

Answer

Explanation:

Step1: Separate variables

For the differential equation $\frac{dy}{dx}=e^{x - 2}y^{2}$, we separate variables by getting all $y$ - terms on one side and all $x$ - terms on the other side. Divide both sides by $y^{2}$ (assuming $y\neq0$) and multiply both sides by $dx$. We get $\frac{1}{y^{2}}dy = e^{x - 2}dx$.

Answer:

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