Question

Can the following equation be solved by separation of the variables?
y''+3y'+y = 0

Answer 1

Sorry, I don't think

Answer 2

Please try this substitution:
\[y(x)=k*e ^{\lambda x}\]
where k is a constant, and \[\lambda \] is another constant to be determined

Answer 3

Please try the substitution tha I have wrote and write the equation which you got after that substitution, note that the variable, in your re-writed equation, must be \[\lambda \]

Answer 4

I get\[y(x) = a \exp(\frac{ -1 }{ 2 }(\sqrt{5}+3)x) +b \exp(\frac{ 1 }{ 2 }(\sqrt{5}-3)x )\]

Answer 5

that's right!