Question:medium
Let \( y = y(x) \) be the solution of the differential equation
\[
x\frac{dy}{dx} - \sin 2y = x^3(2 - x^3)\cos^2 y,\; x \ne 0.
\]
If \( y(2) = 0 \), then \( \tan(y(1)) \) is equal to:
Let \( y = y(x) \) be the solution of the differential equation
\[
x\frac{dy}{dx} - \sin 2y = x^3(2 - x^3)\cos^2 y,\; x \ne 0.
\]
If \( y(2) = 0 \), then \( \tan(y(1)) \) is equal to:
Show Hint
When trigonometric functions appear with derivatives, try converting the equation into a function of \( \tan y \) or \( \sin y \) to simplify.
Updated On: Apr 2, 2026
- \( \dfrac{3}{4} \)
- \( -\dfrac{3}{4} \)
- \( \dfrac{7}{4} \)
- \( -\dfrac{7}{4} \)
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The Correct Option is A
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