`y=e^(3x+7)` then `y_(n)(0)=.........`

If y=x^3(log)_e(1+x) , then y'(0) is equal to.......

If y=e^(x)*e^(x^(2))*e^(x^(3))......e^(x^(n)).... for ^(-)0

If y=3e^(2x)+2e^(3x), show that y_(2)-5y_(1)+6y=0

If y=e^(-x)cos x and y_(n)+k_(n)y=0 where yn=(d^(n)y)/(dx^(n)) and k_(n) are constant n in N then

If y = f (x) is the solution of difierential equation. e ^(y) ((dy)/(dx )-2)=e ^(3x) such that f(0) =0, then f (2) is equal to :

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

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