1. Find the general solution to the following ODE:
y???+ 4y?= sec(2x)
2. Find the solution to the following IVP:
2y??+ 2y??2y= 6x2?4x?1
y(0) = ?32
y?(0) = 5
3. Verify that y1=x1/2ln(x) is a solutionto
4x2y??+y= 0,
and use reduction of order to find a second solutiony2.
4.
Find the general solutions to the following ODEs:
a) y????y?= 0.
b) y??+ 2y?+y= 0.
c) y???4y?+ 13y= 0.
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