Solve a ODE with unknown nonhomogeneous term

Question

I have an ODE which was reduced from a PDE with boundary conditions $A(t)$ and $B(t)$ at $x$ on the boundaries. Is there a way to get a solution for the following

$$\frac{d H(t)}{dt} + \lambda H(t) = -2(A(t)+ B(t))$$

without knowing what $A$ and $B$ are?

Answer 1

From chapter 2 of Antsaklis & Michel's A Linear Systems Primer:

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