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
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:
$\displaystyle m^{2}+2m+\frac{25}{4}=0$
$\displaystyle m=\frac{-3}{2}+2i, \;\ m=\frac{-3}{2}-2i$
Now, you have:
$\displaystyle y=C_{1}e^{\frac{-3}{2}t}cos(2t)+C_{2}e^{\frac{-3}{2}t}sin(2t)$
Now, use your initial condtions to find C1 and C2.