Can someone help me about this equation?

Elimination of arbitrary constant

Y=C-ln x/x

August 28, 2017 - 5:25pm

#1
Tintiiiin

Elimination of arbitrary constant: Y=C-ln x/x

Can someone help me about this equation?

Elimination of arbitrary constant

Y=C-ln x/x

Subscribe to MATHalino.com on

SPONSORED LINKS

We're now on YouTube! Please subscribe.

- Math
- algebra 1
- math
- Sight Distance of Vertical Parabolic Curve
- SOLID GEOMETRY: fly stationed at a point on the circumference of the base of a cylindrical tower
- Steel design
- Differential Equation
- solid geometry
- Solid Geometry
- From a cylindrical jar 4 in. high and 6 in. in diameter, water is poured by tilting the jar until the center of the bottom is at

Here it is.

To eliminate the constant of the equation

$$y = c - \frac{\ln x}{x}$$

Implicitly differentiating the above equation:

$$y' = 0 - d \left (\frac{\ln x}{x}\right)$$ $$y' = 0- \left( \frac{1-\ln x}{x^2}\right)$$ $$y' = \frac{-1+\ln x}{x^2}$$ $$x^2 y' = -1 + \ln x$$

Ultimately, we got a differential equation $x^2 y' = -1 + \ln x.$

Hope it helps.