What is the solution for x*dy=dx,y(-1)=3 ?

The solution for x*dy=dx,y(-1)=3 is y=ln(x)+c_{1}

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x*dy=dx,y(-1)=3

x \cdot d y = d x, y (- 1) = 3

y = ln (x) + c_{1}

Solution steps

x \cdot d y = d x

Let

y

be the dependent variable. Divide by

d x

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

x y^{^{'}} (x) = 1

Isolate

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

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}

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What is the solution for x*dy=dx,y(-1)=3 ?
The solution for x*dy=dx,y(-1)=3 is y=ln(x)+c_{1}