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Popular Calculus >

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

Solution

(x + 1) \frac{d y}{d x} = x

Solution

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

Solution steps

(x + 1) \frac{d y}{d x} = x

Substitute

\frac{d y}{d x}

with

y^{'} (x)

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

Isolate

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

If

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

then

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

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

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

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

Graph

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Frequently Asked Questions (FAQ)

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