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Popular >

(dy)/(dx)=-1/x

Solution

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

Solution

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

Solution steps

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

Substitute

\frac{d y}{d x}

with

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

y^'+y=e^{2t},y(0)=-1

y^{^{'}} + y = e^{2 t}, y (0) = - 1

integral of (1-ln(x))

\int (1 - ln (x)) d x

(\partial}{\partial y}(\frac{e^x+e^y)/2)

\frac{\partial}{\partial y} (\frac{e ^{x} + e ^{y}}{2})

y^{''}+2y^'+y=1,y(1)=1,y^'(1)=0

y^{^{''}} + 2 y^{^{'}} + y = 1, y (1) = 1, y^{^{'}} (1) = 0

limit as x approaches-5+of ((x-5))/(x+5)

x \to - 5 + lim (\frac{( x - 5 )}{x + 5})

Frequently Asked Questions (FAQ)

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