Final answer:
To solve the equation (x³+8x³y²)dx + eˣ⁴ydy = 0, we need to find an implicit solution in the form F(x, y) = C, where C is an arbitrary constant.
Step-by-step explanation:
To solve the equation (x³+8x³y²)dx + eˣ⁴ydy = 0, we need to find an implicit solution in the form F(x, y) = C, where C is an arbitrary constant.
To solve this equation, we can separate the variables and integrate both sides with respect to x and y. Let's start by dividing both sides of the equation by dx and dy:
(x³+8x³y²) + eˣ⁴y * dy/dx = 0
Simplifying the equation, we get:
x³ + 8x³y² + eˣ⁴y * dy/dx = 0
No further simplification is possible, so this is the implicit solution for the given equation.