Homework Statement
Prove that sinh(kt) is of exponential order |k|.
Find M>0, c>=0 and T>0 to show that
|f(t)|= Me^(ct), t>T
Homework Equations
|f(t)|= Me^(ct), t>T
The Attempt at a Solution
I'm looking at the graph of sinhkt (i graphed a few values of k) and indeed it is of an...
Homework Statement
This is the original question:
\frac{d^{2}y}{dx^{2}}-\frac{6x}{3x^{2}+1}\frac{dy}{dx}+\lambda(3x^{2}+1)^{2}y=0
(Hint: Let t=x^{3}+x)
y(0)=0
y(\pi)=02. The attempt at a solution
This might be all wrong, but this is all I can think of
\frac{dt}{dx}=3x^{2}+1
so...
Question:
\int^{1}_{-1} \frac{dx}{(1+x^4)}
I attempt:
u = x^2,
so x= u^1/2
dx= 1/2 u^(-1/2)
Which gives me \int^{1}_{1} \frac{1}{(1+x^4)} * \frac{1}{(2u^1/2)}du, which is 0. Thats not the answer as seen by any graphing utility.
Where is this error? I do not know integration by parts. I just...