Let t = ť -α
Let y = y'- β
where t' and y' are new variables, and α and β are constants to be determined.
Note: dt= dt' and dy = dy'
(t'- α + 3y' -3β -5) dt' + (y'-αβ - t'+αβ+1)dy' =0
(t'+3y' -α -3β-5) dt' +(-t'+y'+α -β +1) dy' = 0 (equation 2)
We want to find the values of α and ...
Given (t-3y-5) dt + (y-t+1) dy =0
introduce a change of variables to transform this ODE into a homogeneous one and solve.