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
Related MCQs
- F(ln a)
- f(a)
- f(e^x)
- f(1/a)
اس سوال کو وضاحت کے ساتھ پڑھیں
- [1 2, 2 1, 1 3] [x1, x2, x3] = [9 7]
- [3 1, 2 1, 1 2] [x1, x2, x3] = [9 7]
- [1 2, 2 1, 1 3] [x1, x2, x3] = [7 9]
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
- d²x/dt² = - m²x
- d²x/dt² = + m²x
- d²x/dt² = ± m²x
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
- 6
- 5
- 4
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
- 2
- -2
- -1
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
Leave a Reply
Your email address will not be published. Required fields are marked *