Determine degree and order of x3dy-dx- y3-y2- y 2 - x 2 -

x^3dy/dx = y^3 + y^2√(y^2 x^2) Degree is oneorder is one. ...

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Order of a Differential Equation

Determine deg...

Question

Determine degree and order of $x^{3} (d y / d x) = y^{3} + y^{2} \sqrt (y^{2} - x^{2})$ .

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x^{3} \frac{d y}{d x} = y^{3} + y^{2} \sqrt{y^{2} - x^{2}}

\frac{x + \frac{d y}{d x}}{y - x \frac{d y}{d x}} = \frac{x {cos}^{2} (x^{2} + y^{2})}{y^{3}}

tan (x^{2} + y^{2}) = \frac{x^{2}}{y^{2}} + c

x d x + y d y = \frac{1}{2} d (x^{2} + y^{2})

\frac{y d x - x d y}{y^{2}} = d (\frac{x}{y})

Find the centroid of the triangle with vertices A $(x_{1}, y_{1})$ , B $(x_{2}, y_{2})$ and C $(x_{3}, y_{3})$ .

(x_{1}, y_{1}), (x_{2}, y_{2})

(x_{3}, y_{3})

\sum (\frac{y_{1} - y_{2}}{x_{1} x_{2}}) = 0

\frac{y_{1} - y_{2}}{x_{1} x_{2}} + \frac{y_{2} - y_{3}}{x_{2} x_{3}} + \frac{y_{3} - y_{1}}{x_{3} x_{1}} = 0

[\frac{x^{3} + y^{3}}{{(x - y)}^{2} + 3 x y}] \div [\frac{{(x + y)}^{2} - 3 x y}{x^{3} - y^{3}}] \times \frac{x y}{x^{2} - y^{2}}

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