Solve the first-order differential equation with initial condition ().

Answer and explanation

Correct answer: D.

  1. Step 1: Separate variables and integrate both sides: .
  2. Step 2: Use the initial condition : . Substituting back gives . Since , taking the principal square root yields .
Answer
.
Why not the others: The linear equation erroneously treats the rate of change as constant; the expression incorrectly sets instead of ; the polynomial integrates the right-hand side while treating as a constant on the left.

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