2. Sample Papers
  3. JEE Main & Advanced

JEE Main & Advanced Sample Paper JEE Main - Mock Test - 10

  • question_answer
    The solution of the differential equation\[{{e}^{\frac{dy}{dx}}}=x+1\], when \[y\left( 0 \right)=3\], is

    A) \[y=x\log x-x+2\]

    B) \[y=(x+1)log|x+1|-x+3\]

    C) \[y=(x+1)log|x+1|+x+3\]

    D) \[y=xlogx+x+3\]

    Correct Answer: B

    Solution :

    [b]: We have, \[{{e}^{\frac{dy}{dx}}}=x+1\] \[\Rightarrow \]\[\frac{dy}{dx}={{\log }_{e}}(x+1)\] \[\Rightarrow \]\[\int_{{}}^{{}}{dy}=\int_{{}}^{{}}{{{\log }_{e}}}(x+1)dx\] \[\Rightarrow \]\[y=(x+1)log|x+1|-(x+1)+c\] When \[y(0)=3\] then, \[3=0-1+c\Rightarrow c=4\] \[\Rightarrow \]\[y=(x+1)log\left| x+1 \right|-x+3\]


You need to login to perform this action.
You will be redirected in 3 sec spinner