JEE Mains · Maths · STD 12 - 9. differential equations
Let \(y=y(x)\) be the solution of the differential equation \(x\frac{dy}{dx}-sin~2y=x^{3}(2-x^{3})cos^{2}y,\) \(x\ne0.\) If \(y(2)=x,\) then \(tan(y(1))\) is equal to
- A \(\frac{3}{4}\)
- B \(\frac{7}{4}\)
- C \(-\frac{7}{4}\)
- D \(-\frac{3}{4}\)
Answer & Solution
Correct Answer
(B) \(\frac{7}{4}\)
Step-by-step Solution
Detailed explanation
\(x \frac{d y}{d x}-\sin 2 y=x^3\left(2-x^3\right) \cos ^2 y\) \(sec^{2}y\frac{dy}{dx}-2~tan~y.\frac{1}{x}=x^{2}(2-x^{3})\) \(tan~y=t \Rightarrow sec^{2}y\frac{dy}{dx}=\frac{dt}{dx}\) \(\frac{dt}{dx}-\frac{2t}{x}=x^{2}(2-x^{3})\) (LDE) I.F.…
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