Question

5y'' + 2y' +20y=cos(t)
Find the steady state solution to the forced equation.

Answer 1

Would the general solution to the equation be of any value?

Answer 2

no i dont think so .. i think its just the steady state solution

Answer 3

general is complementary + particular
complementary is transient
particular is steady state

Answer 4

Plug in A Sin(t)+ B cos(t) into y and solve

Answer 5

y=A sin(t)+ B cos(t)
y'= A Cos(t)-B Sin(t)
y''= -A sin(t)-B cos(t)

Answer 6

5(-A sin(t)-B cos(t))+2(A cos(t)-B Sin(t))+20 (A sin(t)+B cos(t))

-5 A Sin(t)-5 cos(t)+ 2A cos(t)-2B Sin(t)+ 20 A sin(t)+20B cos(t)= cos(t)

Answer 7

find A and b

Answer 8

\[\frac{1}{229} (2 \sin (t)+15 \cos (t))
\]

Answer 9

Of course, one has to do first what @imranmeah91 did above

Answer 10

-5A-2B+20A=0

-5B+2A+20B=1

Answer 11

http://www.wolframalpha.com/input/?i=Solve%5B%7B-5A-2B%2B20A%3D%3D0+%2C-5B%2B2A%2B20B%3D%3D1%7D%2C%7BA%2CB%7D%5D