if i do enough of these problems i will eventually get it.... ok i see that the problem is homogeneous, but why cant it be linear? x dy/dx = ye^(x/y) - x i rewrote it in the form.... dy/dx - (ye^(x/y))/x = -1
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$\displaystyle y'+P(x)y=Q(x)$ is a linear ODE, note that in your rewriting $\displaystyle P(x)$ depends of $\displaystyle x$ and $\displaystyle y,$ so it's not linear.
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