If $X _ { 1 }$ and $X _ { 2 }$ are solutions of the second order system $\mathbf { X } ^ { \prime } = A \mathbf { X }$ and $\mathrm { X } _ { p }$ is a particular solution of $\mathrm { X } ^ { \prime } = A \mathrm { X } + f ( t )$ , then the general solution of $\mathrm { X } ^ { \prime } = A \mathrm { X } + f ( t )$ is
A) $\mathrm { X } _ { 1 } + \mathrm { X } _ { 2 } + \mathrm { X } _ { p }$
B) $\mathbf { X } _ { 1 } + \mathbf { X } _ { 2 } + c _ { 3 } \mathbf { X } _ { p }$
C) $c _ { 1 } \mathbf { X } _ { 1 } + c _ { 2 } \mathbf { X } _ { 2 }$
D) $c _ { 1 } \mathbf { X } _ { 1 } + c _ { 2 } \mathbf { X } _ { 2 } + c _ { 3 } \mathbf { X } _ { p }$
E) $c _ { 1 } \mathbf { X } _ { 1 } + c _ { 2 } \mathbf { X } _ { 2 } + \mathbf { X } _ { p }$

Question

Quizplus · Accepted Answer

The general solution of a nonhomogeneous linear differential equation is the sum of the general solution of the corresponding homogeneous equation and any particular solution of the nonhomogeneous equation. Here, $c_1X_1 + c_2X_2$ represents the general solution of the homogeneous equation, and $X_p$ is a particular solution of the nonhomogeneous equation.

If X1X _ { 1 }X1​ And X2X _ { 2 }X2​

If $X _ { 1 }$ And $X _ { 2 }$