Solve: xdy/dx=1-y^2

Question
Differential equations
asked 2021-01-22
Solve: \(\displaystyle{x}\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}={1}-{y}^{{2}}\)

Answers (1)

2021-01-23
\(\displaystyle{x}\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}={1}-{y}^{{2}}\)
cross-multiply to get,
\(\displaystyle\frac{{1}}{{{1}-{y}^{{2}}}}{\left.{d}{y}\right.}=\frac{{1}}{{x}}{\left.{d}{x}\right.}\)
integrate both sides,
\(\displaystyle\int\frac{{1}}{{{1}-{y}^{{2}}}}{\left.{d}{y}\right.}=\int\frac{{1}}{{x}}{\left.{d}{x}\right.}\)
\(\displaystyle{a}{\text{tanh}{{\left({y}\right)}}}={\ln{{\left({A}{x}\right)}}}\)
\(\displaystyle{y}={\text{tanh}{{\left({\ln{{\left({A}{x}\right)}}}\right)}}}\)
0

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