Finding Particular Solution of a Second Order Differential equation with dsolve

The homogenous equation: 28^(e^(−2x)) − 18(e(−3x))

I found the homogenous solution to the equation, however I am not sure how to find the particular solution when the differential equation is equal to 8. I tried using the dsolve function, however it doesn't give me the correct solution. Apparently the particular solution is supposed to be 4/3.

   y2 = dsolve('D2v + 5*Dv + 6*v = 8')

Answer 1

[Birdman]

Well, it should give you the correct solution. In my computer it worked:

>>syms v(x)
  eq=diff(v,2)+5*diff(v)+6*v==8;
  v(x)=dsolve(eq)

ans =

C1*exp(-2*x) + C2*exp(-3*x) + 4/3

[Jaryd Kynaston-Blake]

now how can get values for C1 & C2 using:

V(0) = V0 % just an arbitrary variable

& t(0) = 0

Sincerely.

[Torsten]

syms v(x) v0
eq = diff(v,2)+5*diff(v)+6*v==8;
Dv = diff(v,x);
cond = [v(0)==v0, Dv(0)==0];
vSol(x) = dsolve(eq,cond)

vSol(x) =