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(1 point) Match the following nonhomogeneous linear equations with the form of the particular solution yp...

(1 point) Match the following nonhomogeneous linear equations with the form of the particular solution yp for the method of undetermined coefficients.

  ?    A    B    C    D      1. y′′+y=t(1+sint)

  ?    A    B    C    D      2. y′′+4y=t2sin(2t)+(5t−7)cos(2t)

  ?    A    B    C    D      3. y′′+2y′+2y=3e−t+2e−tcost+4e−tt2sint

  ?    A    B    C    D      4. y′′−4y′+4y=2t2+4te2t+tsin(2t)


A. yp=t(A0t2+A1t+A2)sin(2t)+t(B0t2+B1t+B2)cos(2t)
B. yp=A0t2+A1t+A2+t2(B0t+B1)e2t+(C0t+C1)sin(2t)+(D0t+D1)cos(2t)
C. yp=Ae−t+t(B0t2+B1t+B2)e−tcost+t(C0t2+C1t+C2)e−tsint
D. yp=A0t+A1+t(B0t+B1)sint+t(C0t+C1)cost

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