Differential Equations: Determine values of r, if possible, so that the differential equation has a solution of the form y = e^(rx). See attached.

Question

Differential Equations:  Determine values of r, if possible, so that the differential equation has a solution of the form y = e^(rx).  See attached.

anonymous · Answer

attachment

anonymous · Answer

write characteristic equation

 s^4- 8s^3-9=0

solve for s.

all solution goes in

$$y= C_1 e^{s_1t}+C_2e^{s_2t}+....$$

anonymous · Answer

They are trying to have us solve it by substituting in the derivatives.  The degree 4 is throwing me off.  Thanks though.

anonymous · Answer

I don't think it is degree 4 , just 4th derivative

anonymous · Answer

:-O    lol.  Duh!  I forgot that is how they designate higher order derivatives.  Thank you! :-)  Now I can work it.  Too bad they won't let me give you a 2nd medal.

anonymous · Answer

that's fine, glad I could help