Second order differential equations of the homogen type
y” (x)+ a y'(x) + by(x) = 0
are possible to solve with the aid of the characteristic equation
r2 + a r +b =0
If this have the roots r1 and r2
the solution is given by
y(x) = Cer1x + Der2 x
If the equation is inhomogenous and the right side is a polynom assume a solution a polynomial of the same degree
If the right side is a trigonometric function assume a as a solution a combination of trigonometric functions.
Ex. Solve the equation y” -3y – 4y = 0
Solve the characteristic equation: r2-3r-4 = 0
r=4 och r = -1.
The general solution is y = Ce-4x + Dex
Where C and D are arbetare constants.