Solve the differential equation dy/dx = 4x^3.

Step 1: Recognize the equation as a direct integration problem.

We are given:
dy/dx = 4x^3

To find y, integrate both sides with respect to x.

Step 2: Integrate both sides.

∫ dy = ∫ 4x^3 dx

Step 3: Apply the power rule for integration.

The power rule states:
∫ x^n dx = x^(n + 1)/(n + 1) + C, for n ≠ -1

Therefore:
∫ 4x^3 dx = 4(x^4/4) + C

Step 4: Simplify.

y = x^4 + C

Step 5: Check the solution by differentiating.

Differentiate y = x^4 + C:

dy/dx = 4x^3

This matches the original differential equation.

Therefore, the general solution is y = x^4 + C.