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mel0
 2 years ago
solve xdy/dxy=x
mel0
 2 years ago
solve xdy/dxy=x

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

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

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

sirm3d
 2 years 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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