Answer to Question #178212 in Differential Equations for Ashweta Padhan

Question #178212

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

y(0)=1

y(infinity )=0


1
Expert's answer
2021-04-15T07:41:01-0400

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: .


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