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let
u=y'
du/dy = d/dy (y') = d/dx(y') . (dx/dy) = y''/y'
y''= u. du/dy
y.y''= (y')^2
y.(u. du/dy) = u^2
∫du/u = ∫dy/y
ln|u| = ln|y| +C'
u= C1.y
dy/dx = C1.y
∫dy/y =∫ C1.dx
ln|y| = C1.x + C2'
y =C2. e^(C1.x)
u=y'
du/dy = d/dy (y') = d/dx(y') . (dx/dy) = y''/y'
y''= u. du/dy
y.y''= (y')^2
y.(u. du/dy) = u^2
∫du/u = ∫dy/y
ln|u| = ln|y| +C'
u= C1.y
dy/dx = C1.y
∫dy/y =∫ C1.dx
ln|y| = C1.x + C2'
y =C2. e^(C1.x)
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