If a-bxey-x-x- then prove that x 3 d 2 y d x 2 - x dy dx -y 2

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Higher Order Derivatives

If a+bxey/x...

Question

If $(a + b x) e^{y / x} = x$ , then prove that $x^{3} \frac{d^{2} y}{d x^{2}} = {(x \frac{d y}{d x} - y)}^{2}$

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If $(a x + b) c \frac{y}{x} = x$ , then show that $X^{3} (\frac{d^{2} y}{d x^{2}}) = {(x \frac{d y}{d x} - y)}^{2}$

(a x + b) e^{y / x} = x

y = x log (\frac{x}{a + b x})

x^{3} \frac{d^{2} y}{d x^{2}} = {(x \frac{d y}{d x} - y)}^{2}

I f (a + b x) e^{\frac{y}{x}} = x t h e n x^{3} \frac{d^{2} y}{d x^{2}} e q u a l s

y = log (\frac{x}{a + b x})^{x}

x^{3} \frac{d^{2} y}{d x^{2}} = (x \frac{d y}{d x} - y)^{2}

(a x + b) e^{\frac{y}{x}} = x

x^{3} \frac{d^{2} y}{d x^{2}} = {(x \frac{d y}{d x} - y)}^{2}

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