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

Practice Questions

Q1
What is the solution of 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 of 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: Write the result of the integration: -1/y = x + C.
  • Step 5: To solve for y, multiply both sides by -1 to get 1/y = -x - C.
  • Step 6: Rewrite the equation as 1/y = -C - x.
  • Step 7: Finally, take the reciprocal to find y: y = 1/(-C - x) or y = 1/(C - x) (by letting C be -C).
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