Mathematics 325
Exam I Summer 2008
ex+
Name:
>.Grov~
4,
1 .(25 pts.) Find the general solution of u, + Zu,+ (2x - y) u + 3xy -2y 2 in the xy -plane. Bonus (10 pts.) Find the solution of this partial differential equation that satisfies the auxiliary condi
Mathematics 325
Exam I Summer 2008
ex+
Name:
>.Grov~
4,
1 .(25 pts.) Find the general solution of u, + Zu,+ (2x - y) u + 3xy -2y 2 in the xy -plane. Bonus (10 pts.) Find the solution of this partial differential equation that satisfies the auxiliary condi
Mathematics 325
Exam I Summer 20 10
Name:
.
1.(25 pts.) (a) Find the characteristic curves of yu, - x u , = 0 in the xy - plane. (b) Sketch and identify two characteristic curves of this partial differential equation. (c) Write the general solution of thi
Mathematics 325
Exam I
Name:
%.&J
1 .(25 pts.) Find all seconddegree polynomial functions of two real variables, u (x,t)=m2+ bxt+ct2+ clk+et+ f where a, b, c, d , e , and f are real constants, which are solutions in the xt -plane of the onedimensional dif