Question

solve the equation:(3x+3xy2+3xy3)dx + (2x2y+3x2y2) dy=0 as an implicit solution in the form F(x,y) = C where c is an arbitrary constant C=?

Answer 1

To solve the given equation, separate the variables and integrate to obtain the implicit solution in the form F(x,y) = C.

Step-by-step explanation:

To solve the given equation, we need to separate the variables and integrate. Rearranging the equation, we have (3x+3xy^2+3xy^3)dx + (2x^2y+3x^2y^2) dy = 0. We can start by dividing through by dx, giving us (3x+3xy^2+3xy^3) + (2x^2y+3x^2y^2) rac{dy}{dx} = 0.

Now, we can rearrange and integrate both sides. Let's integrate the left side with respect to x and the right side with respect to y.

After integrating, the implicit solution in the form F(x,y) = C will be obtained.