Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I have

[tex]

y'' - y' = \frac{1}{e^{x} + 1}

[/tex]

What I did:

[tex]

\lambda^2 - \lambda = 0

[/tex]

[tex]

\lambda_1 = 0

[/tex]

[tex]

\lambda_2 = 1

[/tex]

FSS = [itex][1, e^x][/itex]

[tex]

y = a + be^x

[/tex]

[tex]

y' = a' + b'e^x + be^x

[/tex]

Putting first two terms zero, I get

[tex]

y'' = b'e^x + be^x

[/tex]

[tex]

y'' - y' = b'e^x + be^x - be^x = b'e^x = \frac{1}{e^x + 1}

[/tex]

[tex]

b' = \frac{1}{e^{2x} + e^x}

[/tex]

From the second condition

[tex]

a' + b'e^x = 0

[/tex]

I get

[tex]

a' = -\frac{e^x}{e^{2x} + e^x} = 1 - \frac{e^x}{1+e^x}

[/tex]

Anyway,

[tex]

a' + b'e^x = 0

[/tex]

now isn't true. Where do I do the mistake?

Thank you very much.

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# Simple one on ODE

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