If y = a + bx^2, a, b arbitrary constants, then A. d^2y/dx^2 =2 xy B. x d^2y/dx^2 = y1

Question

If y = a + bx^2, a, b arbitrary constants, then

A. \(\frac{d^2y}{dx^2}=2xy\)

B. \(x\frac{d^2y}{dx^2}=y_1\)

C. \(x\frac{d^2y}{dx^2}-\frac{dy}{dx}+y=y\)

D.\(x\frac{d^2y}{dx^2}=2xy\)

Answer 1

Correct Answer is (C) \(x\frac{d^2y}{dx^2}-\frac{dy}{dx}+y=y\)

Given:

\(\frac{dy}{dx}=2bx\)

\(\frac{d^2y}{dx^2}=2b\neq2xy\)

\(x\frac{d^2y}{dx^2}=2bx\)

\(=\frac{dy}{dx}\)

\(x\frac{d^2y}{dx^2}-\frac{dy}{dx}+y\) \(=2bx-2bx+y\)

= y