(19) (a) Suppsoe that y is a solution of the differential equation ay" + by' + cy = 0. Let z(r) = y(r - ro) where ro is an arbitrary real number. Show that az" + bz' + cz = 0. (b) Let 21 (r) = y1 (x -...

Extracted text: (19) (a) Suppsoe that y is a solution of the differential equation ay" + by' + cy = 0. Let z(r) = y(r - ro) where ro is an arbitrary real number. Show that az" + bz' + cz = 0. (b) Let 21 (r) = y1 (x - ro) and z2(x) = y2(x - xo), where yG = C1y1 + c2y2 is the general solution to ay" + by' + cy = 0. Show that zG = c121 + c222 is also a general solution of ay" + by' + cy = 0.