Question

\frac{dy}{dx}=\frac{xy+3x-y-3}{xy-2x+4y-8} Solve it using variable separation

Differential equations
ANSWERED
asked 2021-02-10
\(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\frac{{{x}{y}+{3}{x}-{y}-{3}}}{{{x}{y}-{2}{x}+{4}{y}-{8}}}}\)
Solve it using variable separation

Answers (1)

2021-02-11
\(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\frac{{{x}{y}+{3}{x}-{y}-{3}}}{{{x}{y}-{2}{x}+{4}{y}-{8}}}}={\frac{{{x}{\left({y}+{3}\right)}-{1}{\left({y}+{3}\right)}}}{{{x}{\left({y}-{2}\right)}+{4}{\left({y}-{2}\right)}}}}\)
\(\displaystyle={\frac{{{\left({y}+{3}\right)}{\left({x}-{1}\right)}}}{{{\left({y}-{2}\right)}{\left({x}+{4}\right)}}}}\)
\(\displaystyle{\frac{{{y}-{2}}}{{{y}+{3}}}}{\left.{d}{y}\right.}={\frac{{{x}-{1}}}{{{x}+{4}}}}{\left.{d}{x}\right.}\)
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