Homogeneous first-order equation and substitution y = vx (If dy/dx depends on y/x alone, set y = vx so dy/dx = v + x dv/dx, then)
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If dy/dx depends on y/x alone, set y = vx so dy/dx = v + x dv/dx, then separate variables in v and x.
What each symbol means
| Symbol | What it stands for |
|---|---|
| F | Any function of a single variable y/x. |
| v | y/x after substitution. |
When to use this
Typically x ≠ 0 domain; check v constant solutions after separation.