# Tagged Questions

The Laplace transform is a widely used integral transform (transformation of functions by integrals), similar to the Fourier transform.

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### How to compute the inverse laplace transform of this term? ${-{{3}\over{10}}s-{{1}\over{5}}\over{(s+1)^2+1}}$

So, I have been asked to solve $y'-2y=e^{-t} *cos(t)$ where $y(0)=-2.$ I applied the Laplace transform, getting $$\mathcal{L}(y)={{-2s^2-3s-3}\over{(s-2)((s+1)^2+1)}}$$ I set up a partial fraction ...
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### Why Fourier transform is not sufficient and we have to use Laplace transform?

Is there an easy way to explain the motivation behind the use of Laplace transform instead of Fourier transform? Isn't that any periodic function can be represented by sines and cosines? Why to ...
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### Can you use Laplace transform to show a function is convex?

First, I should say I just know about Laplace transform through Wikipedia. My question is, Can you use Laplace transform to show a function is convex? If so, is there any link to an example? I have ...
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### N-order differential equations

Suppose that we have n-order differential equation like $$h(x)=?$$ Is it possible to find a general solution for all n? $$(x^n+1).|h'(x)|^n=const.$$.
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### On a second set of calculations for the Buchstab function

In this post I've added simple calculations deduced for the Buchstab function as claims. Question. Can you choose the worst of these claims and show where were my mistakes or inaccurancies? Also ...
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### Solving ode with Laplace transform

What i want to ask is both question 20 and 21 with Laplace transforms Actually i can solve question 20 and 21 with method of undetermined coefficients but . In laplace transform, i don't know how to ...