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## Main Question or Discussion Point

Good day to all,

I encounter this expression in analyzing my equation after transform it using Laplace Transform, to get the answer I have to invert it back, I have no idea on how to find its inversion.

[text]-\text{Cosh}\left[\sqrt{2 s+s^2} x_0\right]+\text{Cosh}\left[s h_0+\sqrt{2 s+s^2} x_0\right]+\text{Sinh}\left[\sqrt{2 s+s^2} x_0\right]-\text{Sinh}\left[s h_0+\sqrt{2 s+s^2} x_0\right][\text]

After looking at the table of Laplace Transforms I just could find the expression of [text]\text{Sinh}[\sqrt{s}][\text] or [text]\text{Cosh}[\sqrt{s}][\text], in my equation there are terms of $\sqrt{2 s+s^2}$, i think because of that make it more difficult, if not i could use convolution theorem and utilize special Laplace transforms properties available in the table.

I do appreciate if someone could give me some advice.... thank you in advance...

I encounter this expression in analyzing my equation after transform it using Laplace Transform, to get the answer I have to invert it back, I have no idea on how to find its inversion.

[text]-\text{Cosh}\left[\sqrt{2 s+s^2} x_0\right]+\text{Cosh}\left[s h_0+\sqrt{2 s+s^2} x_0\right]+\text{Sinh}\left[\sqrt{2 s+s^2} x_0\right]-\text{Sinh}\left[s h_0+\sqrt{2 s+s^2} x_0\right][\text]

After looking at the table of Laplace Transforms I just could find the expression of [text]\text{Sinh}[\sqrt{s}][\text] or [text]\text{Cosh}[\sqrt{s}][\text], in my equation there are terms of $\sqrt{2 s+s^2}$, i think because of that make it more difficult, if not i could use convolution theorem and utilize special Laplace transforms properties available in the table.

I do appreciate if someone could give me some advice.... thank you in advance...

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