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First order ODE Reduced to homogeneous ODE

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.

Solution Preview

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 ...

Solution Summary

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.

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