What is the general solution to the separable differential equation dy/dx = 2x * y for y > 0?
Answer and explanation
Correct answer: C. y = C * e^(x^2)
Separate variables: (1/y) dy = 2x dx. Integrate both sides: integral (1/y) dy = integral 2x dx => ln(y) = x^2 + C1. Exponentiating both sides yields y = e^(x^2 + C1) = e^C1 e^(x^2) = C e^(x^2), where C is an arbitrary positive constant.
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