find the general real solution to the following equation y′′(x) + 2y′(x) + 5y(x) = 0

Question

anonymous · Answer

set up characterestic equation$$m^2+2m+5=0$$$$m=-1\pm2i=a+bi$$so the general real solution will be in the form$$y=e^{ax}(c_1\cos bx+c_2\sin bx)$$

anonymous · Answer

Thanks,already go it thoug....Can i just ask something....How do u knw how many terms u will have in your solution? Does the degree of the characteristic equation tell u tht?

anonymous · Answer

?

turingtest · Answer

if by "terms" you mean number of solutions y1 and y2 from which you can superimpose in the form (i.e. for a second-order equation)$$y=c_1y_1+c_2y_2$$yes, the number of the order equals the number of solutions if it is homogeneous
if it is non-homogeneoues there will be a particular solution as well$$y=c_1y_1+c_2y_2+y_p$$and $y_p$ could have any number of terms, so that is the best answer I can give your question given the wording....
you are confusing the word terms and solutions in this case it seems

anonymous · Answer

yes...thanks I am..I was not sure how to ask..atleast u understood!!

turingtest · Answer

happy to help :)

anonymous · Answer

Can u tell me the diffrence between a particular solution and the homogeousHow does 1 get a particular solution for a DE?

turingtest · Answer

do you know the difference between a homogeneous and non-homogeneous equation?

anonymous · Answer

homogeneous I s zero....
non-homo,not equal zero ..Is that true>?