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Beliebt Rechnen >

(x^2-y^2)y^'=2xy

Lösung

(x^{2} - y^{2}) y^{^{'}} = 2 x y

Lösung

y = \frac{1 + - 4 e ^{2 c_{1}} x ^{2} + 1}{2 e ^{c_{1}}}, y = \frac{1 - - 4 e ^{2 c_{1}} x ^{2} + 1}{2 e ^{c_{1}}}

Schritte zur Lösung

(x^{2} - y^{2}) y^{'} (x) = 2 x y

Solve using substitution:

y = \frac{1 + - 4 e ^{2 c_{1}} x ^{2} + 1}{2 e ^{c_{1}}}, y = \frac{1 - - 4 e ^{2 c_{1}} x ^{2} + 1}{2 e ^{c_{1}}}

y = \frac{1 + - 4 e ^{2 c_{1}} x ^{2} + 1}{2 e ^{c_{1}}}, y = \frac{1 - - 4 e ^{2 c_{1}} x ^{2} + 1}{2 e ^{c_{1}}}

Graph

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