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
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.