[" 10.If "y=e^(" pow ")-1<=x<=1" ,show that "],[(1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)-a^(2)y=0]

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

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

If e^x+e^y=e^(x+y) , prove that (dy)/(dx)=-(e^x(e^y-1))/(e^y(e^x-1)) or, (dy)/(dx)+e^(y-x)=0

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

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

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

If e^(x)+e^(y)=e^(x+y)" then "y_(1)=

If e^(x)+e^(y)=e^(x+y), prove that (dy)/(dx)=-(e^(x)(e^(y)-1))/(e^(y)(e^(x)-1)) or,(dy)/(dx)+e^(y-x)=0

If e^(x) + e^(y) = e^(x + y) , then prove that (dy)/(dx) = (e^(x)(e^(y) - 1))/(e^(y)(e^(x) - 1)) or (dy)/(dx) + e^(y - x) = 0 .

Consider the differential equation y^(2)dx+(x+(1)/(y))dy=0. If y(1)=1, then x is given by: (A) 1-(1)/(y)+((1)/(e^(j)))/(e)(B)4-(2)/(y)-(e^(y))/(e)(C)3-(1)/(y)+(e^(y))/(e)(D)1+(1)/(y)-((1)/(e^(y)))/(e)