General Solutions of Differential Equations?

Daniel S

How would you go about getting the general solutions to second order DE's like this?

Y''-8Y'+17Y=0 and Y''-2Y'-3Y=0

Wrecking my head as I could do these no bother but can't find me feckin' notes on them! The notes on the internet want you to have it in a different format which is throwing me off.

Brussels Sprout

You'll need to form the auxiliary equation from the coefficients of the different terms. The type of general solution that you arrive at will be dependent on the nature of the roots of this equation.

The auxiliary equation for the first one for example would be m^2-8m+17=0

Daniel S

Brussels Sprout wrote: »

You'll need to form the auxiliary equation from the coefficients of the different terms. The type of general solution that you arrive at will be dependent on the nature of the roots of this equation.

The auxiliary equation for the first one for example would be m^2-8m+17=0

Could you help me a bit more? I still don't get it. Even a link to a page that explains it. WolframAlpha's no use to me either.

Brussels Sprout

Have a look at this:

https://www.youtube.com/watch?v=soU-zRdpsoA

Daniel S

Brussels Sprout wrote: »

Have a look at this:

https://www.youtube.com/watch?v=soU-zRdpsoA

Muchas gracias amigo!