MATLAB: Finding Particular Solution of a Second Order Differential equation with dsolve

differential equations

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')

Best Answer

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
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