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What is the solution to the differential equation dy/dx = y^2?

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What’s inside this PDF?

Question: What is the solution to the differential equation dy/dx = y^2?

Options:

  1. y = 1/(C - x)
  2. y = C/(x - 1)
  3. y = Cx
  4. y = e^(x + C)

Correct Answer: y = 1/(C - x)

Solution:

Separating variables and integrating gives y = 1/(C - x).

What is the solution to the differential equation dy/dx = y^2?

Practice Questions

Q1
What is the solution to the differential equation dy/dx = y^2?
  1. y = 1/(C - x)
  2. y = C/(x - 1)
  3. y = Cx
  4. y = e^(x + C)

Questions & Step-by-Step Solutions

What is the solution to the differential equation dy/dx = y^2?
  • Step 1: Start with the differential equation dy/dx = y^2.
  • Step 2: Separate the variables by rewriting the equation as dy/y^2 = dx.
  • Step 3: Integrate both sides. The left side becomes -1/y, and the right side becomes x + C (where C is the constant of integration).
  • Step 4: After integration, you have -1/y = x + C.
  • Step 5: Rearrange the equation to solve for y: y = -1/(x + C).
  • Step 6: To match the short solution format, rewrite it as y = 1/(C - x) by changing the sign.
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