Question #178212

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

y(0)=1

y(infinity )=0

Expert's answer

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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