chemENGINEER
I ran into a 1st order DiffEQ that....



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chemENGINEER
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I cannot figure which method to solve it with (linear, exact, homo, ect) x(dy/dx)=y + sqrt(x^2 + y^2)

chemENGINEER
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\[x \frac{ dy }{ dx }=y + \sqrt( x^2y^2) \]

chemENGINEER
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subtraction not addition, sorry...

Mimi_x3
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homogenous
\(y=ux\)
you have to change it; to seperable

Mimi_x3
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\[\large x\frac{dy}{dx}=y+\sqrt{x^2+y^2}\]
correct?

chemENGINEER
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no x^2y^2 is under the radical, sorry about typo

Mimi_x3
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\[\large x\frac{dy}{dx}=y+\sqrt{x^2y^2}\]???

chemENGINEER
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yes.

Mimi_x3
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so, its homogeous
\(y=ux\)
\[\frac{dy}{dx}=v+x\frac{dv}{dx}\]
are you able to start it?

chemENGINEER
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indeed i have it from here.... thank you for the help!

Mimi_x3
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:)
if you need any help; feel free to ask :)