Question

can anyone help me find the general solution to the 2nd order differential equation
y'' − 5y' + 6y = 3

Answer 1

the auxillary eqn for complementry fuction is
m^2-5m+6=0
(m-3)(m-2)=0
m=2,3

Answer 2

\[y _{c}=C _{1}e ^{2}x+C _{2}e ^{3}x\]

Answer 3

\[y[x]=\frac{1}{2}+e^{2 x} C[1]+e^{3 x} C[2] \]

Answer 4

This is a an undetermined coefficient type problem in case you need to go read your book and review.

Answer 5

mathgirl,
Are you talking to moi?

Answer 6

no darlin, to raetp

Answer 7

robtobey i get the auxilery function and how that works i just dont understand how the =3 part comes into play

Answer 8

A commented Mathamatica solution is attached.