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y^2 dx−x^2 dy = xdy−ydx |
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Answer» y2dx - x2dy = x dy - ydx ⇒ (x2 + x)dy = (y2 + y)dx ⇒ \(\frac{dy}{y(y+1)}=\frac{dx}{x(x+1)}\) ⇒ dy(1/y - 1/(y + 1)) = dx(1/x - 1/(x + 1)) ⇒ log y - log (y + 1) = log x - log (x + 1) + log C ⇒ log(y/y+1) = log(x/x+1) + log C ⇒ log(y/(y+1) x (x+1)/x) = log C ⇒ \(\frac{(x+1)y}{x(y+1)}=C\) ⇒ (x + 1)y = Cx(y + 1) which is solution of given differential equation. |
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