Final answer:
To solve the given differential equation by variation of parameters, find the complementary solution and a particular solution, then combine them to get the general solution.
Step-by-step explanation:
To solve the given differential equation by variation of parameters, we will first find the complementary solution by solving the homogeneous equation y''+y=0. The general solution of this homogeneous equation is y = C1*cos(x) + C2*sin(x), where C1 and C2 are constants. Next, we will find the particular solution by assuming that the particular solution has the form y_p = u(x)*cos(x) + v(x)*sin(x), where u(x) and v(x) are functions to be determined. Substituting this into the original equation and solving for u(x) and v(x), we can find the particular solution. Finally, the general solution of the given differential equation is y = C1*cos(x) + C2*sin(x) + y_p.