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Solve the differential equation dy/dx = 3x^2.

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Question: Solve the differential equation dy/dx = 3x^2.

Options:

  1. y = x^3 + C
  2. y = 3x^3 + C
  3. y = x^2 + C
  4. y = 3x + C

Correct Answer: y = x^3 + C

Solution: 

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

Solve the differential equation dy/dx = 3x^2.

Practice Questions

Q1
Solve the differential equation dy/dx = 3x^2.
  1. y = x^3 + C
  2. y = 3x^3 + C
  3. y = x^2 + C
  4. y = 3x + C

Questions & Step-by-Step Solutions

Solve the differential equation dy/dx = 3x^2.
  • Step 1: Start with the given differential equation: dy/dx = 3x^2.
  • Step 2: To solve for y, we need to integrate both sides of the equation with respect to x.
  • Step 3: Integrate the right side: ∫3x^2 dx. This gives us x^3 + C, where C is the constant of integration.
  • Step 4: The left side, ∫dy, simply gives us y.
  • Step 5: Combine the results from the integration: y = x^3 + C.
  • Differential Equations – Understanding how to solve first-order differential equations by integration.
  • Integration – Applying the rules of integration to find the antiderivative of a polynomial function.
  • Constant of Integration – Recognizing the importance of including the constant of integration (C) in the solution.
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