Second order differential equation

[mr bob]

I just came across this one, was going really well until i came across this one.

(d^2y/dx^2) + (dy/dx) = e^(-x)
m^2 + m = 0
m = -1 and m = 0

Now i get the particular integral
Try y = ke^(-x)
(dy/dx) = -ke^(-k)
(d^2y/dx^2) = ke^(-x)


ke^(-x) - ke^(-x) = e^(-x)

I get stuck here as k-k= 0, not one.

Any help would be greatly appreciated.

 

[topsquark]

I just came across this one, was going really well until i came across this one.

(d^2y/dx^2) + (dy/dx) = e^(-x)
m^2 + m = 0
m = -1 and m = 0

Now i get the particular integral
Try y = ke^(-x)
(dy/dx) = -ke^(-k)
(d^2y/dx^2) = ke^(-x)ke^(-x) - ke^(-x) = e^(-x)

I get stuck here as k-k= 0, not one.

Any help would be greatly appreciated.

Try $$y=axe^{-x} +be^{-x}$$

-Dan