Recent content by Hurry

Hi, I'm currently studying this because I have a test tomorrow but I don't get very well the solution, is there a way to solve it without using the Heaviside step function?

Consider $\begin{align*} & {{u}_{tt}}={{u}_{xx}},\text{ }x\in \mathbb{R},\text{ }t>0 \\ & u(x,0)=0,\text{ }x\in \mathbb{R} \\ & {{u}_{t}}(x,0)=\left\{ \begin{matrix} \sin x,\text{ }\left| x \right|\le \pi \\ 0,\text{ }x\notin [-\pi ,\pi ] \\ \end{matrix} \right. \end{align*} $...

Hi, I have a test tomorrow and I'd like you to guys help me please. Solve the following: $\begin{align*} & {{u}_{tt}}={{u}_{xx}}+1+x,\text{ }0<x<1,\text{ }t>0. \\ & u(x,0)=\frac{1}{6}{{x}^{3}}-\frac{1}{2}{{x}^{2}}+\frac{1}{3},\text{ }{{u}_{t}}(x,0)=0,\text{ }0<x<1. \\ &...