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The error tells you to set option... when done the equation is solved.

y = function('y')(x)
de = diff(y,x)*(4*x+2*y-3) - 2*x-y-1
solution = desolve(de, y,contrib_ode=True)
solution

[-1/5*(4*x + 2*y(x) - 3)*(log(1/(4*x + 2*y(x) - 3) + 1)/(4*x + 2*y(x) - 3) - log(1/(4*x + 2*y(x) - 3))/(4*x + 2*y(x) - 3) - 1) == _C + x]