The general solution of the differential equation \frac{d y}{d x}=\frac{2 x^2-x y-y^2}{x^2-y^2} is [AP EAPCET 22 May 2025 S1]

Correct Answer is : √2log|y2−2x2x2|+log|y−√2xy+√2x|+2√2log|x|=c

\log {| \frac{y^2-2 x^2}{x^2} |}+\sqrt{2} \log {| {y-\sqrt{2} x}/{y+\sqrt{2} x} |}+2 \sqrt{2} \log |x|=c

\sqrt{2} \log {| \frac{y^2-2 x^2}{x^2} |}+\log {| {y-\sqrt{2} x}/{y+\sqrt{2} x} |}+2 \sqrt{2} \log |x|=c

\sqrt{2} \log {| \frac{y^2+2 x^2}{x^2} |}+\log {| {y+\sqrt{2} x}/{y-\sqrt{2} x} |}+2 \sqrt{2} \log |x|=c

\log {| \frac{2 x^2-y^2}{x^2} |}+\sqrt{2} \log {| {y+\sqrt{2} x}/{y-\sqrt{2} x} |}+\log |x|=c

Differential Equations

Section: Mathematics

Question : 17 of 48

Marks: +1, -0

The general solution of the differential equation ‌

=‌

2x2−xy−y2

x2−y2

[AP EAPCET 22 May 2025 S1]

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