# Q. 1# (a−x)dy+(a+y)dx=0(a−x)dy+(a+y)dx=0

Question
Differential equations
Q. 1# $$(a−x)dy+(a+y)dx=0(a−x)dy+(a+y)dx=0$$

2020-11-25
Here the Differential equations is given by
$$(a−x)dy+(a+y)dx=0$$
$$(a−x)dy=−(a+y)dx$$
$$\frac{dy}{a+y}=−\frac{dx}{a−x}$$
$$\frac{dy}{a+y}=\frac{dx}{x−a}$$
$$\int \frac{dy}{a+y}=\int \frac{dx}{x−a}$$
$$\ln(a+y)=\ln(x−a)+\ln c$$
$$a+y=c(x−a)$$
$$y=c(x−a)−a$$
where cc is a arbitrary constant.

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