Which of the following functions are soltuions of the differntial equation y''+y=sin(x)?
a) y=cos(x) b) y=sin(x) c) y=1/2*xcos(x) d) y=1/2*x*sin(x)
The Attempt at a Solution
I'm kind of lost on how to solve this problem. I don't think this is a standard calculus II problem but it was on a packet that we were asked to solve.
I learned from the internet that you can solve a second differential order equation of form
Af''(x) + Bf'(x) + Cf(x) = 0
By setting f'(x) as r_1, f''(x) as r_2, f(x) as 1
Ar^2 + Br + C = 0
and plugging into
y(x) = c_1 e^(r_1*x) + c_2*e^(r_2*x)
were c_1 and c_2 are just some constants that can be solved for if your given initial conditions
I'm unsure how to solve this problem because it's of a different form of
f''(x) + f(x) = sin(x)
I'm unsure what to do about the sin(x) term in this case and not sure what to do sense I don't have initial condition and how to come up with the constant terms as a result...
Thanks for any Help!