Differential Equations JEE Main Solution

JEE MAIN 2025

29-01-2025 SHIFT-1

Question

Let $y = y(x)$ be the solution of the differential equation $\cos x{\left( {{{\log }_{\rm{e}}}(\cos x)} \right)^2}{\rm{dy}} + \left( {\sin x - 3y\sin x{{\log }_{\rm{e}}}(\cos x)} \right){\rm{d}}x = 0,x \in \left( {0,\frac{\pi }{2}} \right)$. If $y\left( {\frac{\pi }{4}} \right) = \frac{{ - 1}}{{{{\log }_{\rm{e}}}2}}$ , then $y\left( {\frac{\pi }{6}} \right)$ is equal to:

Select the correct option:

$\frac{1}{{{{\log }_e}(4) - {{\log }_e}(3)}}$

$\frac{1}{{{{\log }_e}(3) - {{\log }_e}(4)}}$

$\frac{2}{{{{\log }_e}(3) - {{\log }_e}(4)}}$

$ - \frac{1}{{{{\log }_e}(4)}}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution