for n = 1
assume true for ...
How do I prove the conjecture that
d^(n)y
______ = k^(n) y
dx^(n)
The n are in the same position like 2 in the second derivative, d2y/dx2. And the n on the RHS is an exponent, but the y is not.
I know to use induction but I'm stuck at proving P(k+1),
d^(k+1)y
______
dx^(k+1)
Thank you very much!
skeeter does this using induction on n and assuming that dy/dx= ky is that true? You do not mention it in your post but without that conclusion is not true.
The n are in the same position like 2 in the second derivative, d2y/dx2. And the n on the RHS is an exponent, but the y is not.
I know to use induction but I'm stuck at proving P(k+1),
d^(k+1)y
______
dx^(k+1)
Thank you very much!