Final answer:
To find the solution to the given equation, we can integrate both sides of the equation. On the left side, we integrate y³dy and on the right side, we integrate (4 + x²)dx. The solution to the equation is (1/4)y⁴ = (4x + (1/3)x³) + C, where C is the constant of integration.
Step-by-step explanation:
The given equation is dy/dx = (4 + x²)/y³. To find the solution, we can rewrite the equation as y³dy = (4 + x²)dx. Now, we can integrate both sides of the equation. On the left side, we integrate y³dy to get (1/4)y⁴. On the right side, we integrate (4 + x²)dx to get (4x + (1/3)x³). Therefore, the solution to the equation is (1/4)y⁴ = (4x + (1/3)x³) + C, where C is the constant of integration.