yy' + x*e^y = 0
yy' = -x*e^y
ydy/(e^y) = -xdx
Осталось проинтегрировать.
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yy' + x*e^y = 0
yy' = -x*e^y
ydy/(e^y) = -xdx
Осталось проинтегрировать.
∫xdx + ∫(y/e^y)dy=C; x²/2-e^(-y)(y+1)=C.