<p>If dy/dx = (x^2)(y), then y could be:</p>
<p>The answer is marked as 2e^(1/3x^3), but another answer choice is e^(1/3x^3) + 7. Why isn't that the answer?</p>
<p>Well, when you integrate, you get:</p>
<p>lny = (1/3)x^3 + C</p>
<p>When you take exponentials on both sides, you get y = e^(1/3x^3 + C) = Ke^(1/3x^3) (K is just some other arbitrary constant). </p>
<p>You probably forgot that when you take exponentials, the addition gets exponential'd too.</p>
<p>So what happened to C?</p>
<p>K means the same as C; they're both just constants. A constant is a constant is a constant. ubercollegeman probably just wanted to use K, heh. Correct me if I'm wrong. Cheers!</p>
<p>I used K because K = e^C. It's not mathematically logical to denote the two constants as both C when they're different, even though they stand for the same concept.</p>