The solution to the differential equation `ylogy+x y^(prime)=0,` where `y(1)=e ,` is

The solution to the differential equation y log y+xy'=0, where y(1)=e, is

The solution of the differential equation e^(x)dx+e^(y)dy=0 is

The solution of the differential equation e^(x)dx+e^(y)dy=0 is

Solution of the differential equation y(a x y+e^x)dx-e^x dy=0 where y(0)=1 is

Solution of the differential equation (dy)/(dx)+(2y)/(x)=0 , where y(1)=1 , is

Solution of the differential equation (dy)/(dx)+(2y)/(x)=0 , where y(1)=1 , is

The solution of the differential equation y' = (1)/(e^(-y) - x) , is

The solution of the differential equation y^(primeprimeprime)-8y^(primeprime)=0, where y(0)=1/8,y^(prime)(0)=0,y''(0)=1 , is