Toronto Math Forum
MAT2442013S => MAT244 MathTests => Quiz 3 => Topic started by: Victor Ivrii on February 27, 2013, 07:46:41 PM

Post problem and solution

I think the question was
$$
y'''y= 2 \sin t
$$
solution:
$$
r^3  1 = 0 \\
(r+1)(r^2+r+1) = 0\\
r = 1, \frac{1 \pm \sqrt{3} i}{2}\\
y_h = c_1 e^{t} + c_2 e^{ \frac{1 +\sqrt{3} i}{2}t} + c_3 e^{ \frac{1  \sqrt{3} i}{2}t} \\
y_p = A \sin t + B \cos t \\
y_p' = A \cos t  B \sin t \\
y_p'' = A \sin t  B \cos t \\
y_p''' =  A \cos t + B \sin t \\
A = 1, B = 1\\
y = c_1 e^{t} + c_2 e^{ \frac{1 +\sqrt{3} i}{2}t} + c_3 e^{ \frac{1  \sqrt{3} i}{2}t} + \cos t  \sin t
$$

NVM 8)

Just got confirmation that this is a correct problem.