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Solve the differential equation dy/dx = 6x.

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Question: Solve 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 = 3x^2 + C, where C is the constant of integration.

Solve the differential equation dy/dx = 6x.

Practice Questions

Q1
Solve 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

Solve the differential equation dy/dx = 6x.
  • Step 1: Start with the differential equation dy/dx = 6x.
  • Step 2: To solve for y, we need to integrate both sides with respect to x.
  • Step 3: The integral of dy is simply y.
  • Step 4: Now, integrate the right side: the integral of 6x with respect to x is 3x^2.
  • Step 5: Don't forget to add the constant of integration, C, to the result.
  • Step 6: Combine the results to get the final solution: y = 3x^2 + C.
  • Differential Equations – Understanding how to solve first-order differential equations through integration.
  • Integration – Applying integration techniques to find the general solution of a differential equation.
  • Constant of Integration – Recognizing the importance of including the constant of integration (C) in the solution.
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