Question

(D^2-1)y=x-1
Find the general equation by reduction of order

Answer 1

\[m^2-1=0\]

\[m=1\] \[m=-1\]
\[Yc=Ce^x+Ce^{-x}\]

what is next?

Answer 2

to use reduction of order, the right side should be 0

for this i suggest a linear function since y'' will be 0
---> -y = x-1 ----> y = 1-x

combine this with complementary solution to form general equation:
\[y = c_1 e^x + c_2 e^{-x} + 1-x\]