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abb0t
 one year ago
Best ResponseYou've already chosen the best response.1First order linear differential equation. Put it into standard form first by dividing everything by x.

abb0t
 one year ago
Best ResponseYou've already chosen the best response.1You're first step is to find the integrating factor u(x)

abb0t
 one year ago
Best ResponseYou've already chosen the best response.1idk if you're there still or not to proceed explaining this...

abb0t
 one year ago
Best ResponseYou've already chosen the best response.1but your integrating factor is: \[e^{\lnx} = \frac{ 1 }{ x }\] 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: \[\int\limits [\frac{ 1 }{ x }y]'=  \int\limits dx = \frac{ 1 }{ x }y= x+C\] \[y = x^2+Cx\]

sirm3d
 one year ago
Best ResponseYou've already chosen the best response.0the equation should be \[\Large \frac{1}{x}y=\int\frac{1}{x} (1) dx\]

abb0t
 one year ago
Best ResponseYou've already chosen the best response.1@sirm3d could you show him how you got that?

sirm3d
 one year ago
Best ResponseYou've already chosen the best response.0the differential equation is \[y'\frac{1}{x}y=1\] with integrating factor \(1/x\) the resulting equation is \[(1/x)y=\int(1/x)(1)dx\]
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