Final answer:
To find a particular solution for the differential equation y''+5y'+6y=10te^4t, assume a solution of the form y_p = Ate^4t, substitute it into the equation, and solve for the constant A to obtain y_p.
Step-by-step explanation:
To find a particular solution to the second-order linear nonhomogeneous differential equation y''+5y'+6y=10te4t, we look for a solution of the form yp = Ate4t where A is a constant that needs to be determined. First, plug in yp and its derivatives into the differential equation.
After substituting and simplifying, you can solve for A by collecting like terms and equating coefficients. This will give you the particular solution yp.