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The second-order non-homogeneous differential equation y ′−6y′+9y=6x 2+2−12e 3x can be solved using the method of undetermined coefficients. True False

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The second-order non-homogeneous differential equation y ′−6y′+9y=6x 2+2−12e 3x can be solved using the method of undetermined coefficients. True

Second-order non-homogeneous differential equation

The given second-order non-homogeneous differential equation
y' - 6y' + 9y = 6x^2 + 2 - 12e^(3x) can be solved using the method of undetermined coefficients.

This method is typically used to solve linear constant coefficient differential equations with non-homogeneous terms in the form of polynomials or exponential functions.

In this case, the non-homogeneous term contains polynomial and exponential components, which can be handled using the method of undetermined coefficients.

By assuming a particular form for the solution and substituting it into the differential equation, we can determine the coefficients that satisfy the equation.

Therefore, the statement is true.

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