If y = a + bx^2,where a and b are arbitrary c | vedclass

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(B) Given the equation $y = a + bx^2$. First,differentiate with respect to $x$: $\frac{dy}{dx} = \frac{d}{dx}(a + bx^2) = 0 + 2bx = 2bx$. Next,differe

Vedclass · Accepted Answer

$x\frac{d^2y}{dx^2} = \frac{dy}{dx}$

Vedclass · Answer

(B) Given the equation $y = a + bx^2$. First,differentiate with respect to $x$: $\frac{dy}{dx} = \frac{d}{dx}(a + bx^2) = 0 + 2bx = 2bx$. Next,differentiate again with respect to $x$ to find the second derivative: $\frac{d^2y}{dx^2} = \frac{d}{dx}(2bx) = 2b$. Now,consider the expression $x \frac{d^2y}{dx^2}$: $x \frac{d^2y}{dx^2} = x(2b) = 2bx$. Since $\frac{dy}{dx} = 2bx$,we can substitute this into the equation: $x \frac{d^2y}{dx^2} = \frac{dy}{dx}$. Thus,option $B$ is correct.

If $y = a + bx^2$,where $a$ and $b$ are arbitrary constants,then which of the following is true?

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