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Find the general solution of dy/dx = 3x^2. (2020)

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Question: Find the general solution of dy/dx = 3x^2. (2020)

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

Exam Year: 2020

Solution: 

Integrating 3x^2 gives y = x^3 + C.

Find the general solution of dy/dx = 3x^2. (2020)

Practice Questions

Q1
Find the general solution of dy/dx = 3x^2. (2020)
  1. y = x^3 + C
  2. y = 3x^3 + C
  3. y = x^2 + C
  4. y = 3x + C

Questions & Step-by-Step Solutions

Find the general solution of dy/dx = 3x^2. (2020)
  • Step 1: Start with the equation dy/dx = 3x^2.
  • Step 2: Recognize that dy/dx means we need to find the function y by integrating the right side.
  • Step 3: Integrate 3x^2 with respect to x. This means we find the antiderivative.
  • Step 4: The integral of 3x^2 is x^3 + C, where C is the constant of integration.
  • Step 5: Write the general solution as y = x^3 + C.
  • Differential Equations – The question tests the ability to solve a first-order ordinary differential equation using integration.
  • Integration – The solution requires knowledge of basic integration techniques to find the antiderivative of a polynomial function.
  • General Solution – Understanding the concept of a general solution, which includes an arbitrary constant (C) representing the family of solutions.
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