JEE Mains · Maths · STD 12 - 9. differential equations
If \(y=y(x)\) is the solution of the equaiton \(e ^{\sin y} \cos y \frac{ dy }{ dx }+ e ^{\sin y} \cos x =\cos x , y (0)=0\) then \(1+ y \left(\frac{\pi}{6}\right)+\frac{\sqrt{3}}{2} y \left(\frac{\pi}{3}\right)+\frac{1}{\sqrt{2}} y \left(\frac{\pi}{4}\right)\) is equal to
- A \(4\)
- B \(6\)
- C \(2\)
- D \(1\)
Answer & Solution
Correct Answer
(D) \(1\)
Step-by-step Solution
Detailed explanation
Put \(e ^{\text {siny }}= t\) \(\Rightarrow e ^{\sin y} \cos y \frac{ dy }{ d x }=\frac{ dt }{ d x }\) \(\Rightarrow D . E\) is \(\frac{d t}{d x}+t \cos x=\cos x\) \(I.F.\) \(= e ^{\int \cos x dx }= e ^{\sin x }\) \(\Rightarrow\) solution is…
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