overall accuracy: 88.4% record: 33 score: 33 what would be a step in solving the differential equation dy/dx…

overall accuracy: 88.4% record: 33 score: 33 what would be a step in solving the differential equation dy/dx = 3 cos(x)/e^(3y + 3)? ∫1/e^(3y + 3)dy = ∫1/3 cos(x)dx ∫e^(3y + 3)dy = ∫3 cos(x)dx ∫1/e^(3y + 3)dy = ∫3 cos(x)dx ∫e^(3y + 3)dy = ∫1/3 cos(x)dx high score board: overall refresh you must have at least 100 to be on the board. # name record

overall accuracy: 88.4% record: 33 score: 33 what would be a step in solving the differential equation dy/dx = 3 cos(x)/e^(3y + 3)? ∫1/e^(3y + 3)dy = ∫1/3 cos(x)dx ∫e^(3y + 3)dy = ∫3 cos(x)dx ∫1/e^(3y + 3)dy = ∫3 cos(x)dx ∫e^(3y + 3)dy = ∫1/3 cos(x)dx high score board: overall refresh you must have at least 100 to be on the board. # name record

Answer

Explanation:

Step1: Separate variables

For a first - order differential equation of the form $\frac{dy}{dx}=f(x)g(y)$, we rewrite it as $\frac{1}{g(y)}dy = f(x)dx$. Given $\frac{dy}{dx}=\frac{3\cos(x)}{e^{3y + 3}}$, we can cross - multiply to get $e^{3y+3}dy=3\cos(x)dx$.

Answer:

$\int e^{3y + 3}dy=\int3\cos(x)dx$