A homogeneous differential equation of the form M(x, y) dx + N(x, y) dy = 0 can be reduced to a differential equation with separated variables by using the substitution?
- y = vx, dy = vdx + xdv
- x + y = v, dy = dx + dy
- v = x - y, dy = dx - dy
- x + y = y, dy = dx + xdy
Explanation
For a homogeneous DE of the form M(x, y) dx + N(x, y) dy = 0, where M and N are homogeneous functions of the same degree, you use:y = vx, so dy = v dx + x dv
That substitution makes the equation separable in variables v and x.
Last verified on 04-06-2026
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