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

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

Question
Differential equations
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
\(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\frac{{{x}{y}+{3}{x}-{y}-{3}}}{{{x}{y}-{2}{x}+{4}{y}-{8}}}}={\frac{{{x}{\left({y}+{3}\right)}-{1}{\left({y}+{3}\right)}}}{{{x}{\left({y}-{2}\right)}+{4}{\left({y}-{2}\right)}}}}\)
\(\displaystyle={\frac{{{\left({y}+{3}\right)}{\left({x}-{1}\right)}}}{{{\left({y}-{2}\right)}{\left({x}+{4}\right)}}}}\)
\(\displaystyle{\frac{{{y}-{2}}}{{{y}+{3}}}}{\left.{d}{y}\right.}={\frac{{{x}-{1}}}{{{x}+{4}}}}{\left.{d}{x}\right.}\)
0

Relevant Questions

asked 2021-03-22
Solve the equation:
\(\displaystyle{\left({x}+{1}\right)}{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={x}{\left({y}^{{2}}+{1}\right)}\)
asked 2021-05-10
Solve the equation:
\(\displaystyle{\left({a}-{x}\right)}{\left.{d}{y}\right.}+{\left({a}+{y}\right)}{\left.{d}{x}\right.}={0}\)
asked 2021-05-07
Find \(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}\) using the rules for finding derivatives.
\(\displaystyle{y}={\left({2}{x}^{{{2}}}-{6}\right)}{\left({8}{x}^{{{2}}}-{9}{x}+{9}\right)}\)
\(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}=\)
asked 2021-05-23
Find the indicated derivatives.
\(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}\ {\quad\text{if}\quad}\ {y}={2}{x}^{{{3}}}\)
asked 2021-04-27
find the indicated derivatives. \(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}{\quad\text{if}\quad}{y}={2}{x}^{{{3}}}\)
asked 2021-06-07
Given \(\displaystyle{f{{\left({x},{y}\right)}}}={2}{x}^{{{2}}}-{x}{y}^{{{3}}}+{4}{y}^{{{6}}}\), find
\(\displaystyle{{f}_{{\times}}{\left({x},{y}\right)}}=\)
\(\displaystyle{{f}_{{{x}{y}}}{\left({x},{y}\right)}}=\)
asked 2021-06-08
Find the first and second derivatives.
\(\displaystyle{y}={\frac{{{7}{x}^{{{5}}}}}{{{5}}}}-{2}{x}+{9}{e}^{{{x}}}\)
\(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}=\)
asked 2021-02-27
Solve the following differential equations:
\(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\frac{{{x}-{e}^{{-{x}}}}}{{{y}+{e}^{{{y}}}}}}\)
asked 2021-03-06

Give the correct answer and solve the given equation \([x-y \arctan(\frac{y}{x})]dx+x \arctan (\frac{y}{x})dy=0\)

asked 2020-12-01
Given that, \(\displaystyle{y}^{{{\sin{{x}}}}}={x}^{{{{\cos}^{{{2}}}{x}}}},{f}\in{d}:{\frac{{{\left.{d}{x}\right.}}}{{{\left.{d}{y}\right.}}}}\)
...