My Learning Cart

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

Practice Questions

Q1
What is the general solution of 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^2 + C

Questions & Step-by-Step Solutions

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.
No concepts available.
Biology (School & UG)
Biology (School & UG)
Chemistry (School & UG)
Chemistry (School & UG)
Civil Engineering
Civil Engineering
Commerce & Accountancy
Commerce & Accountancy
Computer Science & IT
Computer Science & IT
Current Affairs & GK
Current Affairs & GK
Data Structures & Algorithms
Data Structures & Algorithms
eBooks
eBooks
Electrical & Electronics Engineering
Electrical & Electronics Engineering
English (School)
English (School)
General Aptitude
General Aptitude
General Knowledge
General Knowledge
General Knowledge & Current Affairs
General Knowledge & Current Affairs
Languages & Literature
Languages & Literature
Law & Legal Studies
Law & Legal Studies
Major Competitive Exams
Major Competitive Exams
Mathematics (School)
Mathematics (School)
Mechanical Engineering
Mechanical Engineering
Medical Science
Medical Science
Physics (School & Undergraduate)
Physics (School & Undergraduate)
Quantitative Aptitude & Reasoning
Quantitative Aptitude & Reasoning
Social Science (School)
Social Science (School)
Technical
Technical
Verbal and Reasoning
Verbal and Reasoning
Vocational & Skill Development
Vocational & Skill Development
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely