Final answer:
To find the general solution to a homogeneous differential equation with given constants, apply the quadratic formula to the characteristic equation and use the roots to determine the solution's form, which varies based on whether the roots are real, equal, or complex.
Step-by-step explanation:
In order to solve the homogeneous differential equation, we must first have the explicit form of the equation. Nevertheless, based on the provided context, we can discuss the general approach toward finding solutions to second-order homogenous differential equations. Such equations are typically of the form ay'' + by' + cy = 0, where 'y' is the function of interest and 'a', 'b', and 'c' are constants.
Given constants a = 1.00, b = 10.0, and c = -200, we would normally apply the quadratic formula to the characteristic equation, which in this case is r^2 + br + c = 0, to find the roots 'r'. These roots indicate the nature of the general solution.
If the roots are real and distinct, the general solution would be y = c1*e^(r1*t) + c2*e^(r2*t). If real and equal, the general solution would take the form y = (c1 + c2*t)e^(rt). For complex roots, the general solution would be y = e^(αt)(c1*cos(βt) + c2*sin(βt)), where α is the real part of the roots and β is the imaginary part.
To fully solve the equation, the roots must be calculated and the appropriate form of the solution applied, depending on the nature of the roots.