What is the general solution of the separable differential equation dy/dx = 3x^2 * y for y > 0?
Answer and explanation
Correct answer: D. y = A * e^(x^3)
- Step 1: Separate variables: (1/y) dy = 3x^2 dx. Integrate both sides: integral(1/y dy) = integral(3x^2 dx). Step 2. ln(y) = x^3 + C => y = e^(x^3 + C) = e^C e^(x^3) = A e^(x^3), where A = e^C > 0. *Answer: y = A e^(x^3). Why not the others:** Separating variables requires dividing by y, producing ln(y), not linear integration.
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