# Tagged Questions

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### Prove that the Laplace trasform is a Linear trasformation

Could you help me prove that the Laplace Trasform is a Linear trasformation? Thank you.
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### Laplace transform $y''''+37y''+36y=g(t)$

Hey this problem is making me insane so have at it and let me know what I keep screwing up. Express the solution of the initial value problem in terms of a convolution integral: ...
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### Evaluate $\int_{0}^{\infty}\sqrt{\frac{\sqrt{(a^2-y^2)^2+4y^2}+a^2-y^2}{(a^2-y^2)^2+4y^2}}dy=\sqrt{2}\pi$

Prove or disprove that$$\int_{0}^{\infty}\sqrt{\frac{\sqrt{(a^2-y^2)^2+4y^2}+a^2-y^2}{(a^2-y^2)^2+4y^2}}dy=\sqrt{2}\pi$$ for any $a>1$. I came across with this integral evaluating inverse ...
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### inverse Laplace transfor by using maple or matlab

I want to use inverse Laplace transform to F function by using maple or matlab. However I cannot get any answer. I know the answer from table but I want to use one of softwares. from table: ...
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### Integral equation solve using Laplace transform

How can I solve this integral equation using Laplace transform? $${\int\limits_0^{\infty}\ }\frac{e^{-t}(1-\cos t)}{t}\operatorname d\!t$$ Knowing that $$\mathcal{L}\{\cos t\} = \frac{s}{s^2+1}$$ ...
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### integro-differential equation with application in quantum mechanics

I am trying to solve for the time dynamics for a simple quantum system (two-site system with sinusoidal coupling and a decay parameter on one site) and the math is looking not so simple. Here is the ...
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