If a-b x ey-x-x then x3d2 y-d x2 equals

The correct option is B y/x=log x log(a+bx) Differentiatew.r.t x xdy/dx y/x^2=1/x 1/a+bxb=a/x(a+bx) ∴ x dy/dx y=ax/a+bx→.....(1) Differentiable again w.r.t x ...

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Byju's Answer

Standard XI

Mathematics

Fundamental Laws of Logarithms

If a+b x ey/x...

Question

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

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Solution

The correct option is B
$\frac{y}{x} = l o g x - l o g (a + b x)$
Differentiatew.r.t x
$\frac{x \frac{d y}{d x} - y}{x^{2}} = \frac{1}{x} - \frac{1}{a + b x} b = \frac{a}{x (a + b x)} ∴ x \frac{d y}{d x} - y = \frac{a x}{a + b x} \to . . . . . (1) D i f f e r e n t i a b l e a g a i n w . r . t x x \frac{d^{2} y}{d x^{2}} = \frac{a^{2}}{(a + b x)^{2}} ∴ x^{3} \frac{d^{2} y}{d x^{2}} = \frac{a^{2} x^{2}}{(a + b x)^{2}} = {(\frac{x d y}{d x} - y)}^{2}$

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Similar questions

Q. 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}

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

Q. If

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

, then

x^{3} \frac{d^{2} y}{d x^{2}}

is equal to

Q. If

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

,then

x^{3} \frac{d^{2} y}{d x^{2}}

is equal to

Q. If

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

the show that

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

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If (a+bx)eyx=x then x3 d2ydx2 equals

The correct option is B yx=log x−log(a+bx) Differentiatew.r.t x xdydx−yx2=1x−1a+bxb=ax(a+bx)∴xdydx−y=axa+bx→.....(1)Differentiable again w.r.t xxd2ydx2=a2(a+bx)2∴x3d2ydx2=a2x2(a+bx)2=(xdydx−y)2

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