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UnkleRhaukus
 2 years ago
Can you check my DE solution please
UnkleRhaukus
 2 years ago
Can you check my DE solution please

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UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1\[\begin{align*} xy' &=yxe^{y/x} \\ y' &=y/xe^{y/x} \\ & &&\text{let } y/x=v \\ & &&y=xv \\ & &&y'=v+xv' \\ v+xv'&=ve^v \\ xv'&=e^v \\ {e^{v}}{\dd v}&=\frac{\dd x}x \\ \int{e^{v}}{\dd v}&=\int\frac{\dd x}x \\ e^{v}&=\ln x+c \\ v&=\ln(\ln x+c) \\ y/x&=\ln(\ln x+c) \\ y(x)&=x\ln(\ln x+c) \\ \end{align*}\]
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