Substitution for dy/dx = g(ax + by + c) (When RHS depends only on linear combo ax+by+c, set z = ax+by+c. Then)
jee-mainjee-advanced
When RHS depends only on linear combo ax+by+c, set z = ax+by+c. Then dz/dx = a + b dy/dx, substitute dy/dx from DE to get separable or simpler DE in z and x.
What each symbol means
| Symbol | What it stands for |
|---|---|
| z | Linear combination ax + by + c. |
When to use this
b ≠ 0 typically needed to express dy/dx from dz/dx cleanly; b=0 is already function of x alone.