Can anyone help with this?
x''+9x'+20x=29+20t+6e^(-2t)
i) Obtain the solution x(t) as the sum of the solutions obtained when each component is considered individually in turn.
ii) Solve the equation directly
take for example.
we must find the homogeneous solutions first. that is, solve
we assume a solution of
the characteristic equation is .........you should know how to get this.
or
Thus, the homogeneous solutions are: .
Now we find a particular solution. It must be of the form of the original right hand side, but not the same as the solution to the homogeneous. there is no danger of the latter case here.
so, assume is a particular solution.
and
plug these into the original differential equation, we get:
now simplify and equate coefficients to solve for C.
the solution to the equation will be of the form:
the others are solved in exactly the same way