- #1
sandy.bridge
- 798
- 1
If
[tex]ay+b\int^y_0ydy+cy'=0[/tex]
then
[tex]ay'+by+cy''=0[/tex]
now, let
[tex]y=e^{sx}[/tex]
thus,
[tex]s^2+a/cs+b/c=0[/tex]
and then one solves for s. It is then plugged into what sources are deeming a "general solution"
[tex]y=C_1e^{s_1x}+C_2e^{s_2x}[/tex]
however, none of these texbooks explain or derive where this comes from, and I have not taken any linear algebra or differential equations. Can someone explain where [tex]y=C_1e^{s_1x}+C_2e^{s_2x}[/tex] comes from?
Thanks!
[tex]ay+b\int^y_0ydy+cy'=0[/tex]
then
[tex]ay'+by+cy''=0[/tex]
now, let
[tex]y=e^{sx}[/tex]
thus,
[tex]s^2+a/cs+b/c=0[/tex]
and then one solves for s. It is then plugged into what sources are deeming a "general solution"
[tex]y=C_1e^{s_1x}+C_2e^{s_2x}[/tex]
however, none of these texbooks explain or derive where this comes from, and I have not taken any linear algebra or differential equations. Can someone explain where [tex]y=C_1e^{s_1x}+C_2e^{s_2x}[/tex] comes from?
Thanks!