Decide whether the method of undetermined coefficients together with superposition can be applied to find a particular solution of the given equation. Do not solve the equation.
No, the method of undetermined coefficients together with superposition can’t be applied.
Here, the given differential equation is non-homogeneous.
According to the method of undetermined coefficients, the method of undetermined coefficients applies only to non-homogeneities that are polynomials, exponentials, sine, cosine, or products of these functions.
The given R.H.S. of the equation is not the combination of polynomials t.
From the definition of a polynomial, it should have only non-negative integers as powers.
Therefore, it is not a product of a polynomial and an exponential function.
So, the method of undetermined coefficients cannot be applied.
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