JEE Main & Advanced
Mathematics
Differential Equations
Question Bank
Numerical Value Type Questions - Differential Equations
question_answer
Let \[y=y(x)\] be the solution of the differential equation, \[x\frac{dy}{dx}+y=x\,\,{{\log }_{e}}x,\] \[(x>1).\] If \[2y(2)={{\log }_{e}}4-1,\] and \[y(e)\]is equal to \[\frac{e}{k},\] then find k.