x² dy + xy dx = sqrt(1 – x²y²) dx

solve differential equation​

1 thought on “x² dy + xy dx = sqrt(1 – x²y²) dx<br /><br />solve differential equation​”

1. Step-by-step explanation:

   We have,

   [tex] {x}^{2} dy + xydx = \sqrt{1 – {x}^{2} {y}^{2} } dx \\ [/tex]

   [tex] \implies \: x(x dy + ydx) = \sqrt{1 – {x}^{2} {y}^{2} } dx \\ [/tex]

   [tex] \implies \: x.d(xy) = \sqrt{1 – {x}^{2} {y}^{2} } dx \\ [/tex]

   [tex] \implies \: \frac{d(xy) }{ \sqrt{1 – {x}^{2} {y}^{2} } }= \frac{ dx }{x}\\ [/tex]

   Integrating both sides,

   [tex] \implies \: \int\frac{d(xy) }{ \sqrt{1 – {x}^{2} {y}^{2} } }= \int \frac{ dx }{x}\\ [/tex]

   [tex] \implies \: \sin ^{ – 1} (xy) = ln(x)+c \\ [/tex]

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