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UnkleRhaukus

  • one year ago

Can you check my DE solution please

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  1. UnkleRhaukus
    • one year ago
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    \[\begin{align*} xy' &=y-xe^{y/x} \\ y' &=y/x-e^{y/x} \\ & &&\text{let } y/x=v \\ & &&y=xv \\ & &&y'=v+xv' \\ v+xv'&=v-e^v \\ xv'&=-e^v \\ {e^{-v}}{\dd v}&=-\frac{\dd x}x \\ \int{e^{-v}}{\dd v}&=-\int\frac{\dd x}x \\ -e^{-v}&=-\ln x+c \\ v&=-\ln(\ln x+c) \\ y/x&=-\ln(\ln x+c) \\ y(x)&=-x\ln(\ln x+c) \\ \end{align*}\]

  2. primeralph
    • one year ago
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    Looks good to me.

  3. papsmurf
    • one year ago
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    yea looks pretty good

  4. UnkleRhaukus
    • one year ago
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    Thanks friends !

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