Question

x² dy + xy dx = sqrt(1 – x²y²) dx

solve differential equation​

Answer 1

Step-by-step explanation:

We have,

${x}^{2} dy + xydx = \sqrt{1 - {x}^{2} {y}^{2} } dx$

$\implies \: x(x dy + ydx) = \sqrt{1 - {x}^{2} {y}^{2} } dx$

$\implies \: x.d(xy) = \sqrt{1 - {x}^{2} {y}^{2} } dx$

$\implies \: \frac{d(xy) }{ \sqrt{1 - {x}^{2} {y}^{2} } }= \frac{ dx }{x}$

Integrating both sides,

$\implies \: \int\frac{d(xy) }{ \sqrt{1 - {x}^{2} {y}^{2} } }= \int \frac{ dx }{x}$

$\implies \: \sin ^{ - 1} (xy) = ln(x)+c$