" 20."quad " If "y=e^(a(00-1),-1<=x<=1," show that "(1-x^(2))(d^(2)y)/(dx)-x*(dy)/(dx)-a^(2)y=0

If e^x+e^y=e^(x+y) , show that (dy/dx)=e^(x-y)((e^y-1)/(1-e^x))

Plot y=e^(x),y=e^(x)+1 and y=e^(x)-1.

Plot y=e^(x),y=e^(x)+1 and y=e^(x)-1.

Plot y=e^(x),y=e^(x)+1 and y=e^(x)-1.

Plot y=e^(x),y=e^(x)+1 and y=e^(x)-1.

If the lines joining the points and are perpendicular (0,0),(1,1) and (2,2),(4,y) find y.

The solution of the differential equation dy/dx=e^(y-x)+e^(y+x) ; y(0) = 0 is (1) y=e^x(x+1) (2) e^-y=(e^-x-e^x)+1 (3) e^-y =(e^-x-e^x)-1 (4) e^-y =(e^-x+e^x)+1

Harmonic conjugate of (0,0) wrt to (-1,0) and (2,0) is

If e^(x)+e^(y)=e^(x+y) , prove that : (dy)/(dx)=-(e^(x)(e^(y)-1))/(e^(y)(e^(x)-1)) .

If I = [(1,0),(0,1)] and E = [(0,1),(0,0)] , prove that (a I + bE)^3 = a^3 I + 3a^2 b E .