Q23E - Fundamentals Of Differential Equations And Boundary Value Problems

Question

use the annihilator method to determinethe form of a particular solution for the given equation $\mathit{y}\mathbf{\text{'}}\mathbf{\text{'}}\mathbf{-}\mathbf{5}\mathit{y}\mathbf{\text{'}}\mathbf{+}\mathbf{6}\mathit{y}\mathbf{=}{\mathit{e}}^{\mathbf{3}\mathbf{x}}\mathbf{-}{\mathit{x}}^{\mathbf{2}}$

Step-by-Step Solution

Answer

$y\text{'}\text{'}-5y\text{'}+6y=e^{3x}-x^2$

Step 1: Problem

use the annihilator method to determinethe form of a particular solution for the given equation y''-5y'+6y=e3x-x2

Step 2: Apply DE Theory

Identify the type of differential equation and apply the appropriate solution method.

Step 3: Answer

y ' ' - 5 y ' + 6 y = e 3 x - x 2