Homework Help: Answer need checking!

1. Apr 28, 2006

Hyperreality

I think I've solved this problem, but just need someone to check my answers.

$$u_{x}u+u_{t}=2$$

With initial data

$$u(x,0)=f(x)$$

Use the method of charactersitics $$u(x,t)=u(\xi,\tau)$$, we get

$$\tau_{t}=t$$, $$x_{u}=u$$ and $$u_{\tau}=2$$.

So, by choice of our initial condition,

$$\tau=t$$ and $$u=2t + f(\xi)$$.

Since $$\xi=\xi(x,t)$$. We have

$$u(x,t)=u(\xi(x,t),t)$$

At $$t=0$$ we have $$u(x,0)=u(\xi(x,0),0)$$, therefore

$$x=\xi(x,0)$$

Since we do not know what $$f(x)$$ is, our solution for $$u(x,t)$$ is just

$$u(x,t)=2t+f(\xi(x,t))$$

with initial condition

$$\xi(x,0)=x$$

Is this right??

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