Question

Determine the general solution of the DE 2(2x² + y²)dx - xydy = 0​

Answer 1

Answer:

4x² + y² / x⁴ = C

Step-by-step explanation:

2(2x + y²)dx - xydy = 0

Let y = vx, dy = v • dx + x • dv

2(2x² + v²x²) • dx - x(vx) • (v • dv + x • dv) = 0

==> (4 + v²) • dv = vx • dv

==> dx/x = v • dv/4 + v²

Integrate both sides, we get

ln(4 + v²)/2 = lnx + C

==> 4 + v²/x² = C

==> 4 + y²/x² / x² = C

==> 4x² + y²/x⁴ = C

Answer 2

Answer:

C = 4x² + y² / x⁴

Step-by-step explanation:

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