Question

Let 𝑦 = 𝑦(𝑥) be a solution curve of the differential equation
$𝑥 \frac{𝑑𝑦}{d𝑥} = 𝑦$ ln ( $\frac{y}{x}$ ) , 𝑦 > 𝑥 > 0.
If 𝑦(1) = 𝑒 2 and 𝑦(2) = 𝛼, then the value of $\frac{𝑑𝑦}{𝑑𝑥}$ at (2, 𝛼) is equal to

• A. α
• B. $\frac{α}{2}$
• C. 2α
• D. $\frac{3α}{2}$

Answer 1

Answer: (D)

$\frac{3α}{2}$

Answer 2

The correct option is (D): $\frac{3α}{2}$