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What is the solution to the differential equation dy/dx = 6x?

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Question: What is the solution to the differential equation dy/dx = 6x?

Options:

  1. y = 3x^2 + C
  2. y = 6x^2 + C
  3. y = 2x^2 + C
  4. y = 3x + C

Correct Answer: y = 3x^2 + C

Solution: 

Integrating gives y = (6/2)x^2 + C = 3x^2 + C.

What is the solution to the differential equation dy/dx = 6x?

Practice Questions

Q1
What is the solution to the differential equation dy/dx = 6x?
  1. y = 3x^2 + C
  2. y = 6x^2 + C
  3. y = 2x^2 + C
  4. y = 3x + C

Questions & Step-by-Step Solutions

What is the solution to the differential equation dy/dx = 6x?
  • Step 1: Start with the differential equation dy/dx = 6x.
  • Step 2: To find y, we need to integrate the right side (6x) with respect to x.
  • Step 3: The integral of 6x is (6/2)x^2, which simplifies to 3x^2.
  • Step 4: When we integrate, we also add a constant 'C' to represent any constant value that could be added.
  • Step 5: So, the solution to the differential equation is y = 3x^2 + C.
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