- #1
verd
- 146
- 0
Hey,
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?
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?