Using the method of undetermined coefficients, determine the most suitable choice for $y _ { p }$ given $y ^ {tt } - 3 y ^ { t } - 54 y = x ^ { 2 }$. (You do not need to solve the differential equation.)
A) $y _ { p } = A x + B$
B) $y _ { p } = A x ^ { 2 } + B x + C$
C) $y _ { p } = A x ^ { 3 } + B x ^ { 2 } + C x + D$
D) $y _ { p } = A x ^ { 3 } + C x$
E) $y _ { n } = A x ^ { 2 }$

Question

Quizplus · Accepted Answer

Since the right-hand side of the differential equation is a quadratic function, we should try a quadratic polynomial as our particular solution. Therefore, choice B, $y_p = Ax^2 + Bx + C$, is the best choice.

Using the Method of Undetermined Coefficients, Determine the Most Suitable ypy _ { p }yp​

Using the Method of Undetermined Coefficients, Determine the Most Suitable $y _ { p }$