Question

Let \( y = y(x) \) be the solution of the differential equation \( x^2 dy + (4x^2 y + 2\sin x)dx = 0 \), \( x>0 \), \( y\left(\frac{\pi}{2}\right) = 0 \). Then \( \pi^4 y\left(\frac{\pi}{3}\right) \) is equal to :

• A. 92
• B. 81
• C. 72
• D. 64

Hint:

Always double-check if the differential equation can be turned into an exact derivative like \( \frac{d}{dx}(x^n y) \).

Answer 1

The Correct Option is B