Trivial solution for cosh(x)=0 and sinh(x)=0

[ksukhin]

I'm doing Sturm-Loiuville problems and I need to find the eigenvalues for λ

I'm having difficulty understanding the trivial solutions for the hyperbolic sin and cos when they equal 0.

I know that cos(x)=0 when $x= π/2 + πn = (2n+1)π/2$
sin(x) = 0 when $x=πn$

What about cosh(x) and sinh(x)? Please help

 

[Mark44]

I'm doing Sturm-Loiuville problems and I need to find the eigenvalues for λ

I'm having difficulty understanding the trivial solutions for the hyperbolic sin and cos when they equal 0.

I know that cos(x)=0 when $x= π/2 + πn = (2n+1)π/2$
sin(x) = 0 when $x=πn$

What about cosh(x) and sinh(x)? Please help

$sinh(x) = \frac{e^x - e^{-x}}{2}$
$cosh(x) = \frac{e^x + e^{-x}}{2}$
Clearly cosh(x) is never zero. It's pretty easy to find the zeroes of sinh(x).

 

[mathman]

sinh(x)=0 when x=0.