Solve the following initial value problems:
a) ut+xux= -tu, x is in R, t>0; u(x,0) =f(x), x is in R.
c) ut+ux=-tu, x is in R, t>0; u(x,0)=f(x), x is in R
d)2ut+ux = -2u, x,t in R, t>0; u(x,t)=f(x,t) on the straightline x = t, where f is a given function.
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