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

Question
Differential equations
asked 2020-11-24
Q. 1# \((a−x)dy+(a+y)dx=0(a−x)dy+(a+y)dx=0\)

Answers (1)

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.
0

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