Find the general solution of the differential equation: (2x-y)dy+(x+y-1)dx=0

Question

Please provide a solution thank you!

Answer 1

the d.e. is very close to being an exact equation.

The technique for solving not so hard.

Are you sure the d.e. typed is without a typo?

Answer 2

Notice that the problem is equivalent to

dx = (y – 2x)dt,

dy = (x + y – c)dt

for some auxiliary variable t on which (x,y) depends, and c = 1.

If you diagonalize the matrix (a_ij) with a₁₁ = –2, a₁₂ = a₂₁ = a₂₂ = 1, you can get (x(t),y(t)) as a function of t, c and initial condition (x(0),y(0)).