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Popular Calculus >

xydy=ydx

Solution

x y d y = y d x

Solution

y = ln (x) + c_{1}

Solution steps

x y d y = y d x

Let

y

be the dependent variable. Divide by

d x

:

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

x y y^{^{'}} (x) = y

Isolate

y^{'} (x) : y^{'} (x) = \frac{1}{x}

If

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

then

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

y = \int \frac{1}{x} d x

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

y = ln (x) + c_{1}

Graph

Popular Examples

area 4/x , 4/(x^2),x=7

a re a \frac{4}{x}, \frac{4}{x ^{2}}, x = 7

9y^{''}-y=xe^{x/3}

9 y^{^{''}} - y = x e^{\frac{x}{3}}

implicit (dy)/(dx),x+y=xy

im pl i c i t \frac{d y}{d x}, x + y = x y

derivative of 2x^2-1/x

\frac{d}{d x} (2 x^{2} - \frac{1}{x})

integral from 0 to 8 of 1

\int_{0}^{8} 1

Frequently Asked Questions (FAQ)

What is the solution for xydy=ydx ?
The solution for xydy=ydx is y=ln(x)+c_{1}