Answer to Question #178212 in Differential Equations for Ashweta Padhan

Question

Solve -y^''-2y^'+2y = e^-2x

y(0)=1

y(infinity )=0

Answer 1

Solution:

Characteristic equation:

;

;

; .

The general solution of the homogeneous differential equation:

Let's find a partial solution of the non-homogeneous equation in the form

Substitute , , into the origin differential equation:

The general solution of the non-homogeneous differential equation:

Let's apply conditions:

(because if then )

Answer: .