What is the general solution of the differential equation dy/dx = 3x^2?

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Question: What is the general solution of the differential equation dy/dx = 3x^2?

Options:

Correct Answer: y = x^3 + C

Solution:

Integrating both sides gives y = ∫3x^2 dx = x^3 + C.

What is the general solution of the differential equation dy/dx = 3x^2?

What is the general solution of the differential equation dy/dx = 3x^2?

Step 1: Start with the given differential equation: dy/dx = 3x^2.
Step 2: To find y, we need to integrate both sides of the equation with respect to x.
Step 3: Write the integral: y = ∫3x^2 dx.
Step 4: Calculate the integral of 3x^2. The integral of x^n is (x^(n+1))/(n+1), so for 3x^2, it becomes 3 * (x^(2+1))/(2+1) = 3 * (x^3)/3 = x^3.
Step 5: Add the constant of integration, C, to the result: y = x^3 + C.
Step 6: This is the general solution of the differential equation.

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