PROBLEM 4E

In Problems 1–8, decide whether or not the method of undetermined coefficients can be applied to find a particular solution of the given equation.

Step 1:

In this problem, we have to determine whether the method of undetermined coefficients can be applied to find a particular solution of the given equation.

x’’+5x’-3x=3t

Step 2:

No, we can not find a particular solution of the given equation.

As we know, the method of the undetermined coefficients can be used to find the particular solution for a differential equation of the form

ay’’+by’+cy=Pm(t)ert [method to undetermined coefficients]

Where Pm(t) is a polynomial of degree m, use the form

yp(t)=ts(Am tm+...........A1t+A0)ert

If r is not a root of the auxiliary equation then take s=0;

If r is simple root of the auxiliary equation take s=1…

Therefore the particular solution to the differential equation will be

ay’’+by’+cy=Pm(t)et cos+Qn(t)et sin where