# Math Help - Need Help Using Complex Exponentials To Solve Differential Equation

1. ## Need Help Using Complex Exponentials To Solve Differential Equation

Hi,

Can someone help me with the following?

Use complex exponentials to find the solution of the differential equation

((d^2)y(t)/d(t^2)) + (3dy(t)/dt) + (25/4)y(t) = 0

such that y(0) = 0 and dy/dt = 1 for t = 0.

2. Use your auxiliary equations to find the roots of the quadratic:

$m^{2}+2m+\frac{25}{4}=0$

$m=\frac{-3}{2}+2i, \;\ m=\frac{-3}{2}-2i$

Now, you have:

$y=C_{1}e^{\frac{-3}{2}t}cos(2t)+C_{2}e^{\frac{-3}{2}t}sin(2t)$

Now, use your initial condtions to find C1 and C2.