ODE2.1

From Example Problems
Jump to: navigation, search

y''+3y'+y=0\,

Set up and solve the characteristic equation.

m^{2}+3m+1=0\,

m={\frac  {-3\pm {\sqrt  {9-4}}}{2}}={\frac  {-3}{2}}\pm {\frac  {{\sqrt  {5}}}{2}}=m_{1},m_{2}\,

So the solution is

y=c_{1}e^{{m_{1}x}}+c_{2}e^{{m_{2}x}}\,

Ordinary Differential Equations

Main Page