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JEE Main & Advanced Sample Paper JEE Main Sample Paper-34

  • question_answer
    Let \[y=f\left( x \right)\]satisfy the differential equation \[\frac{dy}{dx}=\frac{x+y}{x},\] \[y(1)=1\] then \[y\left( \frac{1}{e} \right)\] is equal        

    A)  \[2e\]                                  

    B)  \[\frac{2}{e}\]

    C)  0                                            

    D)  \[\frac{1}{e}\]

    Correct Answer: C

    Solution :

    \[\frac{dy}{dx}=1+\frac{y}{x}\]             (Homogenous differential equation)             \[\Rightarrow \,f(x)\,=x+x\,In\,x.\].


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