Question

Solve xp² – 2yp + ax = 0 :

• A. y² = 3cx + c²
• B. y² = cx + c²
• C. 2y = cx² + a/c
• D. None of these

Answer 1

Answer: (C)

2y = cx² + a/c

Answer 2

The given equation can be written as; y = $\frac{xp}{2}$ + $\frac{ax}{2p}$

$\frac{dy}{dx}$ = $\frac{p}{2}$ + $\frac{x}{2}$ . $\frac{dp}{dx}$ + $\frac{a}{2p}$ – $\frac{ax}{2p^{2}}$ . $\frac{dp}{dx}$

Ž p(p² – a) = x(p² – a) .$\frac{dp}{dx}$

Ž $\frac{dp}{dx}$ = $\frac{p}{x}$ Ž p = cx.

(The equation p² – a = 0 given us singular solution in which we are not interested).

The substitute p in (i) we get the required solution;

2y = cx² + $\frac{a}{c}$