AP EAMCET · Maths · Differential Equations
The solution of the equation \(\frac{d y}{d x}+2 y \tan x=\sin x\) satisfying \(y=0\) when \(x=\frac{\pi}{3}\), is
- A \(y=2 \sin ^2 x+\cos x-2\)
- B \(y=2 \sin ^2 x-\cos x-2\)
- C \(y=2 \cos ^2 x-\sin x+2\)
- D \(y=2 \cos x-\sin ^2 x-1\)
Answer & Solution
Correct Answer
(A) \(y=2 \sin ^2 x+\cos x-2\)
Step-by-step Solution
Detailed explanation
Given, differential equation is \[ \frac{d y}{d x}+2 y \tan x=\sin x \] Here, \(P=2 \tan x\) and \(Q=\sin x\) \[ \begin{array}{ll} \therefore & I . F=e^{\int 2 \tan x d x} \\ & =e^{2 \ln |\sec x|}=e^{\ln \sec ^2 x}=\sec ^2 x \end{array} \] Now, required solution is,…
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