" I."y=e^(x)+1

The differential equation which represents the family of curves y=e^(C x) is y_1=C^2y b. x y_1-I n\ y=0 c. x\ I n\ y=y y_1 d. y\ I n\ y=x y_1

If y = (e^(x)-e^(-x))/(e^(x)+e^(-x)) then prove that y = (e^(2x)-1)/(e^(2x)+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.

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

The area bounded by the curves y=x e^x ,y=x e^(-x) and the line x=1 is 2/e s qdotu n i t s (b) 1-2/e s qdotu n i t s 1/e s qdotu n i t s (d) 1-1/e s qdotu n i t s

The area bounded by the curves y=x e^x ,y=x e^(-x) and the line x=1 is 2/e s qdotu n i t s (b) 1-2/e s qdotu n i t s 1/e s qdotu n i t s (d) 1-1/e s qdotu n i t s

The area bounded by the curves y=x e^x ,y=x e^(-x) and the line x=1 is 2/e s qdotu n i t s (b) 1-2/e s qdotu n i t s 1/e s qdotu n i t s (d) 1-1/e s qdotu n i t s

Let y=y(x) , y(1)=1 and y(e)=e^(2) .Consider J=int(x+y)/(xy)dy , I=int(x+y)/(x^(2))dx J-I=g(x) and g(1)=1 then the value of g(e) is