Final answer:
To find the complementary function of the differential equation y" y = csc(x), we first find the general solution of the homogeneous equation y" y = 0. The complementary function is y_c(x) = C1e^x + C2e^-x.
Step-by-step explanation:
The differential equation y" y = csc(x) can be solved using variation of parameters. To find the complementary function, we first find the general solution of the homogeneous equation y" y = 0. The characteristic equation is r^2 - 1 = 0, which has roots r = ±1. Therefore, the complementary function is y_c(x) = C1e^x + C2e^-x, where C1 and C2 are constants.