Tagged Questions

31 views

Laplace transform of product of two function

Consider the following integral of product of two function $$\int_0 ^t f(s)g(s-t)ds$$ i want to know the laplace transform of above term w.r.t t. if $g(s-t)$ is replaced by $g(t-s)$, there is a ...
53 views

183 views

Prove that the Laplace trasform is a Linear trasformation

Could you help me prove that the Laplace Trasform is a Linear trasformation? Thank you.
41 views

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: ...
82 views

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 ...
99 views

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: ...
59 views

71 views

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 $$\mathcal{L}\{\cos t\} = \frac{s}{s^2+1}$$ ...