Question

Solve the following differential equation: y′′ 4y=sin3x answer: y(x)= c1 note: you can eam partial credit on this problem.

Answer 1

To solve the differential equation y'' - 4y = sin(3x), we can use the method of undetermined coefficients. The general solution to the differential equation is y(x) = C1 + C2e^(2x) + (1/4)cos(3x).

Step-by-step explanation:

To solve the differential equation y'' - 4y = sin(3x), we can use the method of undetermined coefficients. Since sin(3x) is a trigonometric function, our guess for the particular solution would be of the form y_p(x) = A sin(3x) + B cos(3x). Plugging this into the differential equation and solving for A and B, we find that A = 0 and B = -1/4. Therefore, the general solution to the differential equation is y(x) = C1 + C2e^(2x) + (1/4)cos(3x).