If (x - y)e^{x/(x - y)} = k,then: | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given the equation: $(x - y)e^{x/(x - y)} = k$. Taking the natural logarithm on both sides: $\ln(x - y) + \frac{x}{x - y} = \ln k$. Differentiatin

Vedclass · Accepted Answer

$y\frac{dy}{dx} + x - 2y = 0$

Vedclass · Answer

(B) Given the equation: $(x - y)e^{x/(x - y)} = k$. Taking the natural logarithm on both sides: $\ln(x - y) + \frac{x}{x - y} = \ln k$. Differentiating both sides with respect to $x$: $\frac{1}{x - y}(1 - \frac{dy}{dx}) + \frac{(x - y)(1) - x(1 - \frac{dy}{dx})}{(x - y)^2} = 0$. Multiply the entire equation by $(x - y)^2$: $(x - y)(1 - \frac{dy}{dx}) + (x - y) - x(1 - \frac{dy}{dx}) = 0$. $(x - y) - (x - y)\frac{dy}{dx} + x - y - x + x\frac{dy}{dx} = 0$. Combine the terms involving $\frac{dy}{dx}$: $(-x + y + x)\frac{dy}{dx} + (x - y + x - y - x) = 0$. $y\frac{dy}{dx} + x - 2y = 0$.

If $(x - y)e^{x/(x - y)} = k$,then:

Similar Questions

If ${2^x} + {2^y} = {2^{x + y}}$,then $\frac{dy}{dx} = $

If $\sin y = x \cos (a + y),$ then $\frac{dy}{dx} = $

For $x>1$,if $(2x)^{2y} = 4e^{2x-2y}$,then $(1+\log 2x)^2 \frac{dy}{dx}$ is equal to

If $\log \sqrt{x^2+y^2}=\tan ^{-1}\left(\frac{x}{y}\right)$,then $\frac{d y}{d x}$ is equal to

If $x^3+y^3=3axy$,then at $\left(\frac{3a}{2}, \frac{3a}{2}\right)$ the value of $3ay^{\prime \prime}+40$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module