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Solution of dy/dx = ky (k > 0) represents
AExponential growth
BLinear decay
CPeriodic motion
DConstant velocity
Answer & Solution
Correct answer: A. Exponential growth
1. Solving dy/dx = ky: ∫dy/y = ∫k dx ⇒ ln|y| = kx + C ⇒ y = A·e^(kx).
2. Since k > 0 the solution grows exponentially with x.
3. Used in compound interest, population growth, capital accumulation.
4. Hence (B) is correct.
_Source: Maharashtra Balbharati Std XII Mathematics & Statistics (Commerce), Ch 9 "Differential Equations", §9.2 ¶§9.2_
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