What is the solution to the equation dy/dx = -5y?

What is the solution to the equation dy/dx = -5y?

Step 1: Recognize that the equation dy/dx = -5y is a separable differential equation.
Step 2: Rewrite the equation to separate the variables: dy/y = -5 dx.
Step 3: Integrate both sides: ∫(1/y) dy = ∫-5 dx.
Step 4: The left side integrates to ln|y| and the right side integrates to -5x + C, where C is a constant.
Step 5: Write the equation from the integration: ln|y| = -5x + C.
Step 6: Exponentiate both sides to solve for y: |y| = e^(-5x + C).
Step 7: Rewrite e^C as a new constant, which we can call C: |y| = Ce^(-5x).
Step 8: Since y can be positive or negative, we can drop the absolute value: y = Ce^(-5x).

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