Question

Solve the given differential equation by undetermined coefficients: y'' - 2y' + 50y = ex cos(7x)

Options:
a. y(x) = Ae^(25x)cos(7x) + Be^(25x)sin(7x)
b. y(x) = Ae^(25x)sin(7x) + Be^(25x)cos(7x)
c. y(x) = Ae^(25x)cos(7x) + Be^(25x)cos(7x)
d. y(x) = Ae^(25x)sin(7x) + Be^(25x)sin(7x)

Answer 1

To solve the differential equation by undetermined coefficients, assume a particular solution, find its derivatives, substitute them back into the equation, solve for the coefficients, and combine the particular solution with the general solution of the homogeneous equation.

Step-by-step explanation:

To solve the given differential equation by undetermined coefficients, we start by assuming a particular solution of the form y_p = Ae^(25x)sin(7x) + Be^(25x)cos(7x). Taking the derivatives of y_p, we substitute them back into the differential equation and solve for the coefficients A and B. After finding the values of A and B, we can write the general solution in the form y(x) = y_h + y_p, where y_h is the general solution of the homogeneous equation.