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Question

Question: The solution curve of \(\frac{dy}{dx}\)= \(\frac{y^{2} - 2xy - x^{2}}{y^{2} + 2xy - x^{2}}\), y(–1) ...

The solution curve of dydx\frac{dy}{dx}= y22xyx2y2+2xyx2\frac{y^{2} - 2xy - x^{2}}{y^{2} + 2xy - x^{2}}, y(–1) = 1 is-

A

A parabola

B

Ellipse

C

Circle

D

Straight line

Answer

Straight line

Explanation

Solution

Solving the homogeneous equation, by using
y = vx, we find the solution x + y = c(x2 + y2) y(–1) = 1 Ž x + y = 0 which is a straight line.