2nd order non-homogenous Equations

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Last updated 6:44 PM on 4/13/26
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5 Terms

1
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General final form

y = yc + yp

yc= C1(y1(t) + C2(y2(t)

2
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if non homogenous part = t2

Ansatz: y = At2 + Bt + C

3
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if non homogenous part has cos(kt) or sin(kt)

Ansatz: y= ACos(kt) + BSin(kt)

4
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What if our compimentary solution and ansatz overlap?

just multiply by “t”

so it becomes : y= Af(x) * t or Af(x) * t2

5
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What if there are multiple functions in the nonhomogenous part?

y = yc + yp1 + yp2

  • So we just solve each function seperately and add them all up at the end !