Find the gene solution by first placing the left side on z and solving the characteristic equation:

y + y = 0

r 2 + 1 = 0

r = 0 Â, Â ± i

y (h) = CÃ Â, sin (x) + CÃ Âcos (x)

Now find the corresponding solution with an indefinite number. Note that we need to multiply each solution by x so that the solution is linearly independent:

y = x [Salt (x) + Bcos (x)]

y = salty (x) + Bcos (x) + x [Acos (x) Bsin (x)]

y = Acos (x) Bsin (x) + Acos (x) Bsin (x) + x [Salt (x) Bcos (x)]

y = 2Acos (x) 2Bsin (x) Axsin (x) Bxcos (x)

2Acos (x) 2Bsin (x) = sin (x) + 0cos (x)

2B = 1

B = 1/2, A = 0

y (p) = xcos (x) / 2

The general solution is made up of the number of genes and their associated solutions:

y = CÃ Â, sin (x) + CÃ scos (x) xcos (x) / 2

y [x] = 1/2 (x Cos [x] + 2 C [1] Cos [x] + 2 C [2] Sin [x])

Hi