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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 11

  • question_answer
    The solution of differential equation \[\frac{dy}{dx}=-\left( \frac{y+\sin x}{x} \right)\] satisfying condition \[y(0)=1\] does not pass through the point

    A) \[(\pi ,\,-2/\pi )\] 

    B) \[(\pi /2,-2/\pi )\]

    C) \[(-\pi /2,2/\pi )\] 

    D) None of these

    Correct Answer: D

    Solution :

    [d] \[\frac{dy}{dx}=-\left( \frac{y+\sin x}{x} \right)\] \[\Rightarrow \,\,\,-x\,dy=ydx+\sin x\,dx\] \[\Rightarrow \,\,\,-\sin x\,dx=x\,\,dy+y\,\,dx\] \[\Rightarrow \,\,-\sin x\,dx=d(xy)\] \[\Rightarrow \,\,\cos x=xy+x\] (Integrating both sides) Since \[y(0)=1,\,\,c=1.\] \[\therefore \,\,\cos x=xy+1\]


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