Let yxbe a solution of the differential equation.1+exy1+yex=1 If y0=2 , then which of the following statements is (are) true?

dydx+ex1+exy=11+exI·F=e∫ex1+ex=1+ex∴Solution isy1+ex=x+cGiven (x,y)=(0,2)⇒2(2)=0+c⇒c=4∴The solution is y1+ex=x+4⇒y=x+41+ex⇒y(-4)=0Now dydx=1+ex-(x+4)ex1+ex2             =1+ex-xex-4ex1+ex2             =1-xex-3exLet dydx=1-(x+3)ex=0⇒1x+3=ex which has a solution in (-1,0)⇒yx has a critical point in -1,0∴options (1) and (3) are correct.