If `y=a+b x^2,\ a ,\ b` arbitrary constants, then `(d^2y)/(dx^2)=2\ x y` (b) `x(d^2y)/(dx^2)=(dy )/(dx)` (c) `x(d^2y)/(dx^2)-(dy)/(dx)+y=0` (d) `x(d^2y)/(dx^2)=2\ x y`

Explanation

Correct option is B)
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y=a+b x^{2} `
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y^{prime}=2 b x `
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Rightarrow 2 b=frac{y^{prime}}{x} `
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y^{prime prime}=2 b=frac{y^{prime}}{x} `
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Rightarrow x frac{d^{2} y}{d x^{2}}=frac{d y}{d x}`
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