First-order Nonlinear Equation with Linear Coefficients

**mafra** · September 12th 2011, 07:33 PM

How do I solve this one?

(2x - y + 4)dy + (x - 2y + 5)dx = 0

**Ackbeet** · September 13th 2011, 01:53 AM

Originally Posted by mafra

How do I solve this one?

(2x - y + 4)dy + (x - 2y + 5)dx = 0

Find the point of intersection of the two lines 2x - y + 4 = 0, and x - 2y + 5 = 0. Suppose that intersection occurs at the point $(x_{0},y_{0}).$ Then do the substitution $u=x-x_{0}$ and $v=y-y_{0}.$

The result of this substitution should result in a recognizeable type of DE. What do you get?

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