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So I solved this one linear DE and the answer I got isn't the same as the one in the back of my textbook... And I'm not sure why. I thought I was doing this right. Could someone tell me what I'm doing wrong?

Here's what I'm given:

[tex]x^{2}y'+xy=1[/tex]

[tex]\frac{dy}{dx}+\frac{x}{x^{2}}y=\frac{1}{x^{2}}[/tex]

[tex]\frac{dy}{dx}+\frac{1}{x}y=\frac{1}{x^{2}}[/tex]

[tex]integrating-factor-p=\frac{1}{x}[/tex]

[tex]integrating-factor\rightarrow e^{\int p(x) dx}=e^{\int \frac{1}{x}dx}= e^{lnx}=x[/tex]

[tex](xy)'=\frac{1}{x^{2}}[/tex]

[tex]xy=\int x^{-2}dx=\frac{-1}{x}+C[/tex]

[tex]y=\frac{-1}{x^{2}}+\frac{C}{x}[/tex]

That's what I get.

The answer in the textbook is:

[tex]y=x^{-1}lnx+Cx^{-1}[/tex]

Which is similar but not the same... What'd I do wrong?

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# Diff EQ - Simple Linear ODE

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