Is my charastic equation for y''-4y' +5y =0 correct?

[RadiationX]

I'm trying to rewrite my notes from my differential equations class last week. my proffesor asked us to write the charastic equation of this:y''-4y' +5y =0 is this correct?
e^{2t}(C_1\cos{t} + C_2\sin{t})

 

[HallsofIvy]

No, it's not- it's not even an equation! I would suggest you look up "characteristic equation" in your textbook.

 

[RadiationX]

No, it's not- it's not even an equation! I would suggest you look up "characteristic equation" in your textbook.

i meant this.y=e^{2t}(C_1\cos{t} + C_2\sin{t})

 

[arildno]

The characteristic equation is what you elsewhere call the auxiliary equation, if I'm not mistaken.

 

[mathwonk]

x^2 - 4x + 5, i.e. make every derivative a power, so you get x^2 -4x + 5x^0

or just substitute y = e^(rt) then perform the derivatives in the given differential equation and you get the characteristic equation out front in terms of the variable r this time.