Q27E - Fundamentals Of Differential Equations And Boundary Value Problems

Question

use the annihilator method to determinethe form of a particular solution for the given equation.

$y\text{'}\text{'}+2y\text{'}+2y=e^{-x}cosx+x^2$

Step-by-Step Solution

Answer

$y_p\left(x\right)=c_1+c_{2}x+c_3{x}^2+c_{6}x{e}^{-x}\cos x+c_{7}x{e}^{-x}\sin x$

Step 1: Problem

use the annihilator method to determinethe form of a particular solution for the given equation.y''+2y'+2y=e-xcosx+x2

Step 2: Apply DE Theory

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

Step 3: Answer

y p ( x ) = c 1 + c 2 x + c 3 x 2 + c 6 x e - x cos x + c 7 x e - x sin x