use thr method of undetermined to coefficent to answer this question please. The

Question

use thr method of undetermined to coefficent to answer this question please.

The particular sol.yp & the nonhomogeneous part g(x) have the same form; this method is called the method of undetermined coefficient & can only be used if: The coefficients of the linear ODE,ak, k = 0,1..., n, are constant. The nonhomogeneous part, g(x) can only have the following forms Polynomial function. Sine or cosine function (sin (betax) or cos(betax)). Exponential einfinityx. Or a finite sum or product of the above 3 function types. Find a particular solution to die non-homogeneous differential equation

Explanation / Answer

2x' + x = 3t^2

particular solution is

Xp(t) = A*t^3 + Bt^2 +Ct + D

Xp'(t) = 3At^2 + 2Bt + C

put it in equation

2*(3At^2 + 2Bt + C) + A*t^3 + Bt^2 +Ct + D = 3t^2

At^3 + (6A+B)t^2 + (4B+C)t + (D+2C) = 3t^2

A=0

B=3

4B+C=0

C=-12

D+2C=0

D=24

so particular solution is

Xp(t) = 3t^2 -12t + 24

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.