• April 22nd 2009, 03:03 AM
revolution2000
If I have the second order differential equation

y'' + y = 0

The auxilliary equation is

m^2 + m = 0

The two solutions are therefore

m = 0, -1

so

y = A*exp(0*x) + B*exp(-1*x)

Is this correct?

My notes say the solution is

y = C1*cos(x) + C2*sin(x)

• April 22nd 2009, 03:45 AM
mr fantastic
Quote:

Originally Posted by revolution2000
If I have the second order differential equation

y'' + y = 0

The auxilliary equation is

m^2 + m = 0 Mr F says: This is wrong. This is the auxillary equation for y'' + y' = 0.

The two solutions are therefore

m = 0, -1

so

y = A*exp(0*x) + B*exp(-1*x)

Is this correct?

My notes say the solution is

y = C1*cos(x) + C2*sin(x)

The auxillary equation for y'' + y = 0 is $m^2 + 1 = 0$.