f(x)

Trial y(x)

Notes

3

y

5x+7

Ax+b

Polynomial of degree one, so Ax+b

3x^2 - 2

ax^2 + bx + c

sin4x

A(cos 4x + B sin 4x)

e^5x

K e^5x

(9x-2) e^5x

(Ax+B) e^5x

Product of an exponential and polynomial

e^3x sin4x

e^3x (Acos 4x + Bsin 4x)

5x sin4x

(Ax+B) sin4x + (cx+d) cos 4x

Xe^3x

e^3x [(ax+b) sin 4x + (cx+d) cos 4x)