Question

Consider the equation: ż= λz + g(t) where λ ∈ C and g(t) is a continuous complex function of real variable. Derive the variation of constants formula for finding a particular solution of the eqn.

Answer 1

We will assume a particular solution
\(z_p=Ag(t)\)
If we substitute this into the equation we get
\(Ag(t)=\lambda Ag(t)+g(t) \implies A(g(t)-\lambda g(t))=g(t) \implies A=\frac{1}{1-\lambda}.\)