Question

By eliminating the arbitrary constants $A$ and $B$ from $y = Ax^{2} + Bx$, the differential equation obtained is

• A. $\dfrac{d^{2}y}{dx^{2}} = 0$
• B. $x^{2}\dfrac{d^{2}y}{dx^{2}} - 2x\dfrac{dy}{dx} + 2y = 0$
• C. $\dfrac{d^{2}y}{dx^{2}} = 0$
• D. $x^{2}\dfrac{d^{2}y}{dx^{2}} + y = 0$

Hint:

To form a differential equation from a family with $n$ arbitrary constants, differentiate $n$ times then eliminate the constants algebraically.

Answer 1

The Correct Option is B