
Let $ y(x) $ be the solution of the differential equation $$ x^2 \frac{dy}{dx} + xy = x^2 + y^2, \quad x > \frac{1}{e}, $$ satisfying $ y(1) = 0 $. Then the value of $ 2 \cdot \frac{(y(e))^2}{y(e^2)} $ is ________.
Alcohol is a derivative of water (H2O) that has one, two, or more hydroxyl groups that are attached to a carbon atom of a hydrocarbon chain (an alkyl group). It is one of the most common organic compounds used in sweeteners, fragrances, and medicine.
Read More: Types of Alcohol