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Popular Calculus >

(dy)/(dx)= k/x

Solution

\frac{d y}{d x} = \frac{k}{x}

Solution

y = k ln (x) + c_{1}

Solution steps

\frac{d y}{d x} = \frac{k}{x}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = \frac{k}{x}

If

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int \frac{k}{x} d x

\int \frac{k}{x} d x = k ln (x) + c_{1}

y = k ln (x) + c_{1}

Graph

Popular Examples

(\partial)/(\partial x)(10e^{x^7y})

\frac{\partial}{\partial x} (10 e^{x^{7} y})

tangent of 1.8e^{2x}-45

t an g e n t 1.8 e^{2 x} - 45

derivative of y=(sqrt(x))/(6+x)

d er i v a t i v e y = \frac{x}{6 + x}

sum from n=0 to infinity of (-5/4)^{-2n}

n = 0 \sum \infty (- \frac{5}{4})^{- 2 n}

limit as h approaches 0 of (a^h-1)/h

h \to 0 lim (\frac{a ^{h} - 1}{h})

Frequently Asked Questions (FAQ)

What is the solution for (dy)/(dx)= k/x ?
The solution for (dy)/(dx)= k/x is y=kln(x)+c_{1}