Rearrange them carefully

Calculus Level 3

If $\dfrac {dy}{dx}$ is directly proportional to $\dfrac yx$ , then is $y$ directly proportional to a positive power of $x$ , or is $y$ inversely proportional to a positive power of $x$ ?

y

is directly proportional to a positive power of

x

y

is inversely proportional to a positive power of

x

1 solution

Aditya Narayan Sharma
Jul 29, 2016

$\displaystyle \frac{dy}{dx}=k \frac{y}{x} \implies \frac{dy}{y}=\frac{kdx}{x} \implies \ln y=\ln(x^k c)$ ,So we have $y$ varies directly with $x^k$ .

Rearrange them carefully

1 solution

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