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Variable Separable Method

x+y dx-dy = ...

Question

$(x + y) (d x - d y) = d x + d y .$

A

log (x + y) = x + y + c .

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B

log (x + y) = x - y + c .

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C

log (x + y) = x - y - c .

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D

None of these

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Solution

The correct options are
B $log (x + y) = x - y - c .$
C $log (x + y) = x - y + c .$
Given, $(x + y) (d x - d y) = d x + d y .$
$(x + y + 1) d y = (x + y - 1) d x$
$\frac{d y}{d x} = \frac{x + y - 1}{x + y + 1} .$
$\Rightarrow \frac{d x + d y}{x + y} = d x - d y .$
Integrating we get,
$log (x + y) = x - y + c .$

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Similar questions

d x + d y = (x + y) (d x - d y) \Rightarrow y + log (x + y) = x + C

is the solution of differential equation

The general solution of differential equation $\frac{d y}{d x} = l o g x$ is

d x + d y = (x + y) (d x - d y)

then fine the value of log(x+y).

x^{y} = e^{x - y}

\frac{d y}{d x} = \frac{l o g x}{(1 - l o g x)^{2}}

.

y = \sqrt{log x + 2 \sqrt{log x + 2 \sqrt{log x + \dots \infty}}}

\frac{d y}{d x}

x = 1

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