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4. a) solve the ff: Initial Value Problem: Eqtn : 2ut + XUx =0 U(X,0) =...

4. a) solve the ff: Initial Value Problem:

Eqtn : 2ut + XUx =0

U(X,0) = f(X)

b) Assuming f is C1,verify that u(x,t) =   f (xe^ -t/2 ) is a solution.

5) a) Solve the Initial Value problem:

Eqtn : 2ut + XUx =0

  U(X,0) = -X^2 +2X,

ON THE DOMAIN 0 < x< 2 , t>2

b ) DRAW THE GRAPHS OF THE SOL. U(X,ti) as a function of X, FOR ti= 0, 0.1, 0.5, 1.0

c) HOW DO SUCH GRAPHS CHANGE AS ti increases ?

Note: please disregard the question that I posted yesterday 9/6... i messed up.

thanks

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