Thread: 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.

Thanks in advance

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





Now, you have:



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