Find the order of the family of curves `y=(c_1+c_2)e^x+c_3e^(x+c_4)`

The differential equation which represents the family of curves y=c_1e^(c_2x) where c_1 and c_2 are arbitrary constants , is :

The order of the differential equation obtained by eliminating arbitrary constants in the family of curves c_(1)y=(c_(2)+c_(3))e^(x-c_(4)) is

The differential equation corresponding to the family of curves y=e^x (ax+ b) is

The orthogonal trajectories of the family of curves y=Cx^(2) , (C is an arbitrary constant), is

The order of the differential equation y=C_(1)e^(c_(2)+x)+C_(3)e^(c_(4)+x is

The differential equation representing the family of curves y^2=2c(x+sqrtc) , where c gt 0 , is a parameter is of order and degree as follows :

Draw the curve y=e^(x)

The order of the differential equation y=C_(1)e^(C_(2)+x)+C_(3)e^(C_(4)+x) is

Find the second order derivative if y= e^(2x)

The area of the figure bounded by the curves y=e^x , y=e^(-x) , and st. line x=1 is :