- #36
AiRAVATA
- 173
- 0
Well, you propose (like in any linear second order ode with constant coefficients) an exponential solution [itex]y(x)=e^{rx}[/itex], and then find out what is the value of [itex]r[/itex], i.e.
[tex]y''(x)+y(x)=(r^2+1)e^{rx}=0.[/tex]
That way, [itex]r=\pm i[/itex] and the solution is [itex]y(x)=Ae^{ix}+Be^{-ix}[/itex]. As you only want real solutions, then [itex]y(x)=C\cos x+D\sin x[/itex].
You should really check a book on ODE's. I recommend you the one written by Boyce and DiPrima Elementary Differential Equations. It should be in your library.
[tex]y''(x)+y(x)=(r^2+1)e^{rx}=0.[/tex]
That way, [itex]r=\pm i[/itex] and the solution is [itex]y(x)=Ae^{ix}+Be^{-ix}[/itex]. As you only want real solutions, then [itex]y(x)=C\cos x+D\sin x[/itex].
You should really check a book on ODE's. I recommend you the one written by Boyce and DiPrima Elementary Differential Equations. It should be in your library.