Math differential equation problem

When you submit your solutions, make sure they are clear, organized, and legible. Clearly mark your final
answer. Show all your work for full credit.
Points: Work as many problems as you wish. The available points for each problem are provided. The points will be added
to your quiz point total.
1. (1 point) Determine the largest region in the xy – plane for which the given initial value problem would have a unique
solution
y
0 =
p
(x − 1)y, y(2) = 1
2. (1 point) Find the general solution of the given ODE
y
00 + 4y = (x
2 − 3) sin(2x)
3. (1 point) Find the general solution of the given ODE
y
00 + 3y
0 + 2y = sin(e
x
)
4. (1 point) Find the particular solution of the given initial value problem
y
000 + 2y
00 − 5y
0 − 6y = 0, y(0) = y
0
(0) = 0, y00(0) = 1
5. (1 point) Find the general solution of system

0 =


−1 0 0
2 −5 −6
−2 3 4

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