Solve the following differential equations using Taylor series
centered at 0. It’s enough to find the recurrence relation and the
first 3 terms of the series.
(a) y''− 2y' + y = 0
(b) y'' + xy' + 2y = 0
(c) (2 + x^2 )y'' − xy'+ 4y = 0
Find a general solution to the differential equation using the
method of variation of parameters.
y''+ 25y= sec5t
The general solution is y(t)= ___
y''+9y= csc^2(3t)
The general solution is y(t)= ___
Find the general solution of the following
differential equations (complementary function
+ particular solution). Find the particular solution by inspection
or by (6.18), (6.23),
or (6.24). Also find a computer solution and reconcile differences
if necessary, noticing
especially whether the particular solution is in simplest form [see
(6.26) and the discussion
after (6.15)].
(D2+2D+17)y = 60e−4x sin 5x