Final answer:
To solve the given differential equation, you can assume a solution of the form y=e^{rx}, where r is a constant. By substituting this solution back into the equation and solving the characteristic equation, you can find the general solution to the differential equation.
Step-by-step explanation:
The given differential equation is:
{d^{2} y}{d x^{2}}+2 {d y}{d x}+2 y=5 s
To solve this differential equation, we can assume a solution of the form y = e^{rx}, where r is a constant.
Taking the second derivative of y and substituting it back into the equation, we get a characteristic equation: r^2 + 2r + 2 = 0.
Solving this equation gives us two complex roots, which can be written as: r = -1 + i and r = -1 - i.
The general solution to the differential equation is then: y = C_1 e^{-x} cos(x) + C_2 e^{-x} sin(x) + 5, where C_1 and C_2 are arbitrary constants.