## mel0 Group Title solve xdy/dx-y=-x one year ago one year ago

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1. abb0t Group Title

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

2. abb0t Group Title

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

3. abb0t Group Title

sorry p(x)*

4. abb0t Group Title

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

5. abb0t Group Title

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. sirm3d Group Title

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

7. abb0t Group Title

@sirm3d could you show him how you got that?

8. sirm3d Group Title

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