2nd Order differential eqn: x"(t) + 4x'(t) - 5x(t) = 9

uberathlete

New member
Joined
Jan 16, 2006
Messages
48
Hi everyone. I'm having trouble solving this 2nd order DE:

x"(t) + 4x'(t) - 5x(t) = 9

If there was a 0 instead of the 9, then I could solve it cuz it's just a homogeneous equation. But in this case, it's something other than 0. I've looked at some texts and websites on non-homogeneous problems but they always illustrate problems with a function on the right hand side instead of a constant. If anyone could enlighten me as to how to solve equations like the above (ie. with a constant on the RHS) it'd be much appreciated. Thanks!
 
Use undetermined coefficients

\(\displaystyle \L\\m^{2}+4x-5=0\)

\(\displaystyle x=-5 \;\ and \;\ 1\)

\(\displaystyle \L\\C_{1}e^{-5t}+C_{2}e^{t}\)

\(\displaystyle y_{p}=A\)

\(\displaystyle {-}5A=9\)

\(\displaystyle A=\frac{-9}{5}\)

So, you have:

\(\displaystyle \L\\C_{1}e^{-5t}+C_{2}e^{t}-\frac{9}{5}\)
 
Top