# Tagged Questions

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### Dirac Delta Function, Initial Value Problem

Hi I finished this IVP but I cant seem to get the right answer can someone give me some advice as to where I went wrong and point me in the right direction as to how to fix it. Here is the problem and ...
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### Solving and graphing an IVP involing unit step function

Im trying to solve this ODE and find a simplified expression for $x(t)$. $$\ddot x+4x=-2\sum_{n=1}^{4} e^{in\pi}u(t-n\pi);\space x(0)=0=\dot x(0),i=\sqrt{-1}$$ First i found the the laplace ...
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### Convolution, indicator function

I need to calculate $(f*f)(x)$ of $f(x) = 1_{[0,1]}(x)$, which is the indicator function defined with Calculating the integral $(f*f)(x) = \int_{0,}^{x}1_{[0,1]}(t) \cdot1_{[0,1]}(x-t) dt$ gives ...
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### Solving initial value problem using Laplace Transform

Use Laplace transform to solve the following initial–value problems. a). $y'' + y = e^{−t}\cos 2t, \\ y(0) = 2, y′(0) = 1$ After using the concept of partial fraction and using Elementary Laplace ...
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### Laplace question continued (partial fractions)

Last night I attempted and successfully finished (with the help of stackexchange) the first part to this question on laplace transformations: Laplace question - help needed The second part to this ...
### Laplace transform of $|\sin(t)|$
There's already an answer to this, but I'm curious as to why my method of solving doesn't work. I take the integral where $\sin{t}$ is positive and the negative integral where it is negative: ...