JEE Main & Advanced Sample Paper JEE Main - Mock Test - 39

  • question_answer
    The solution of differential equation \[x\cos x\frac{dy}{dx}+(x\sin x+\cos x)=1\] is

    A) \[xy\,\sec x=\tan x+c\]  

    B) \[xy\,\tan x=\sec \,x+c\]    

    C) \[y\,\sec x=x\tan x+c\]  

    D) \[y\tan x=x\sec x+c\]

    Correct Answer: A

    Solution :

    [a] We have \[\frac{dy}{dx}+y\left( \tan x+\frac{1}{x} \right)=\frac{1}{x\cos x}\] \[I.F.={{e}^{\int{\left( \tan x\frac{1}{x} \right)\,dx}}}=x\,\sec x\] Therefore, solution is: \[y\times (x\sec x)=\int{\frac{1}{x\cos x}}\times (x\sec x)\,dx\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,xy\sec x=\tan x+c\]

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