Answer to Question #155719 in Differential Equations for Yash

Question

Linear differential equation with constant coefficient

d³y/dx³-13dy/dx+12y

Answer 1

Solution

For solving differential equation

d³y/dx³-13dy/dx+12y =0

we get the characteristic polynomial

s³ -13*s+12=0

In another form

(s-1)*(s² +s-12)=0 => Roots s₁ = 1, s₂ = 3, s₃ = -4.

The superposition principle for homogeneous equations then gives us that the general solution to the DE is

y(x) = C₁*e^x+C₂*e^3x+C₃*e^-4x , where C₁,C₂,C₃ are arbitrary constants.  

Answer

y(x) = C₁*e^x+C₂*e^3x+C₃*e^-4x