Solve the initial value problem below. Indicate the correct steps, in order, that you would use to solve the problem. All the steps might not be used. y′′−2y′+y= sec^2(t), y(0) = 1, y′(0) = 0. (Note:...

Solve the initial value problem below. Indicate the correct steps, in order, that you would use to solve the problem. All the steps might not be used.

y′′−2y′+y= sec^2(t), y(0) = 1, y′(0) = 0.

(Note: you do not need to solve the problem!)

I. Find the general solutiony= c₁y₁+ c₂y₂
to the homogeneous equation y′′−2y′+y= 0.

II. Use the initial conditions to find c₁
and c₂.

III. Use the Method of Undetermined Coefficients to find a particular solution to the nonhomogeneous equation  y′′−2y′+y= sec^2(t).

IV. Use Variation of Parameters to find a particular solution to the nonhomogeneous equation.  y′′−2y′+ y= sec^2(t)