" (i) "quad e^(x)+ce^(y)=1

Find the differential equation: (i) e^(x)+ce^(y)=1(ii)y=2(x^(2)-1)+ce^(-x^(2)))

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

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)) or,(dy)/(dx)+e^(y-x)=0

The solution of the equation (e^x+1)ydy+(y+1)dx=0 , is (A) e^(x+y)=C(y+1)e^x (B) e^(x+y)=C(x+1)(y+1) (C) e^(x+y)=C(y+1)(1+e^x) (D) e^(xy)=C(x+y)(e^x+1)

The solution of the differential equation (dy)/(dx)+1=e^(x+y), is a. (x+y)e^(x+y)=0 b. (x+C)e^(x+y)=0 c. (x-C)e^(x+y)=1 d. (x+C)e^(x+y)+1=0

The solution of the differential equation (dy)/(dx)+1=e^(x+y), is (x+y)e^(x+y)=0b(x+C)e^(x+y)=0c*(x-C)e^(x+y)=1d(x-C)e^(x+y)+1=0

The value of integral int e^(x)((1)/(sqrt(1+x^(2)))+(1)/(sqrt((1+x^(2))^(5))))dx is equal to e^(x)((1)/(sqrt(1+x^(2)))+(1)/(sqrt((1+x^(2))^(3))))+ce^(x)((1)/(sqrt(1+x^(2)))-(1)/(sqrt((1+x^(2))^(5))))+ce^(x)((1)/(sqrt(1+x^(2)))+(1)/(sqrt((1+x^(2))^(5))))+c none of these

(1 + e^(x/y)) dx + e^(x)/(y)(1 - (x)/(y)) dy = 0