2nd order nonhomogeneos differential equations with initial conditions

[pedro123]

I have a problem which in involves a second order differential equations with imaginary roots and I can seem to know how to finish the problem.

d^2y/dt^2 +15y =cos 4t+2 sin t

this is what I got so far


r^2+15=0 for the homogeneous part

r=+-(√15)

Yh=C1cos√15+C2sin√15

now is where I get stuck

 

[SteamKing]

You've got to use the initial conditions to solve for C1 and C2 in order to complete the homogeneous solution. Then, you get to find the particular solution for in inhomogeneous equation.

 

[pedro123]

yes I know but can you explain how

i know i need to have a particular solution for cos 4t+2 sin t
but i don't know how to set up

 

[Mark44]

Problems such as these should be posted in the Homework & Coursework section, not in the technical math sections. I am closing this thread.