Clairaut's differential equation (If y is linear in x and p = dy/dx with coefficients depending only on p)
jee-mainjee-advanced
If y is linear in x and p = dy/dx with coefficients depending only on p, general solution is replace p by arbitrary constant c: y = cx + f(c). Singular solution from envelope p-discriminant.
What each symbol means
| Symbol | What it stands for |
|---|---|
| p | dy/dx. |
| f(p) | Function of p only appearing additively with xp. |
When to use this
Standard Clairaut form; distinguish general vs singular solutions in advanced problems.