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 straight
line x = t, where f is a given function.