Question

D³y/dx³-13dy/DX+12y=0​

Answer 1

Hye user!

As we know that this is a 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*ex+C2*e3x+C3*e-4x , where C1,C2,C3 are arbitrary constants.    

y(x) = C1*ex+C2*e3x+C3*e-4x

Answer 2

Answer in the figure

Hope it helps you