## anonymous 3 years ago solve xdy/dx-y=-x

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1. abb0t

First order linear differential equation. Put it into standard form first by dividing everything by x.

2. abb0t

You're first step is to find the integrating factor u(x)

3. abb0t

sorry p(x)*

4. abb0t

idk if you're there still or not to proceed explaining this...

5. abb0t

but your integrating factor is: $e^{-\ln|x|} = \frac{ 1 }{ x }$ I'm going to skip the work for the next few steps, you can use it as a reference to absolutely check your work, but you SHOULD see that you get product rule as a result. Therefore: $[\frac{ 1 }{ x }y]'=-1$ Next, take the integral: $\int\limits [\frac{ 1 }{ x }y]'= - \int\limits dx = \frac{ 1 }{ x }y= -x+C$ $y = -x^2+Cx$

6. anonymous

the equation should be $\Large \frac{1}{x}y=-\int\frac{1}{x} (1) dx$

7. abb0t

@sirm3d could you show him how you got that?

8. anonymous

the differential equation is $y'-\frac{1}{x}y=-1$ with integrating factor $$1/x$$ the resulting equation is $(1/x)y=\int(1/x)(-1)dx$