Question

Solve the equation.

(x³+8 x³ y²) d x+eˣ⁴ y d y=0
An implicit solution in the form F(x, y)=C is ___=C, where C is an arbitrary constant.

Answer 1

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.