Final answer:
Yes, the method of undetermined coefficients together with superposition can be applied to find a particular solution of the given equation.
Step-by-step explanation:
The method of undetermined coefficients together with superposition can be applied to find a particular solution of the given equation if the right-hand side of the equation is a linear combination of known functions. In this case, the right-hand side has terms involving t², e⁻²ᵗ, sin3t, cos4t, and 10ᵗ. Since these are known functions, the method of undetermined coefficients can be used.
To solve the equation using this method, we would assume a particular solution in the form of:
y_p(t) = At²e⁻²ᵗ + Btsin3t + Ctcos3t + Dte⁻²ᵗ + Etcos4t + Ft
We would then substitute this particular solution into the given equation, solve for the coefficients A, B, C, D, E, and F, and obtain the particular solution.