Problem 9. (8 points) (1) (3 points) Identify those below that are linear PDEs. altar -47 -(x-2y (a) ay 7 ат от - 2x + 3

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Problem 9. (8 points) (1) (3 points) Identify those below that are linear PDEs. altar -47 -(x-2y (a) ay 7 ат от - 2x + 3y = 0 ax (b) zor I + 3 sin(t)- (c) 1987-4) --" sin) (d) d -2T + x-3y - (c) at we have: (2) (5 points) For one-dimensional parabolic PDE a T- TT-27+T- Explicit method: T- TT-27 + *! Implicit method: (Ary Crank-Nicolson (CN) method: 7;'! -T! T.:-27/' +7.7% -21," + Ar -O.SK Ar Fill the blanks below with either "Explicit", "Implicit", or "CN". (a) ar method approximates ar att by centered finite difference ar method approximates ar att" by forward finite difference. (b) (c) In (d) In method, ar? is calculated at time the a't method, ax? is calculated at time t=" a'r method, ar is taken as the average between t= and t="#l. (e) In