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Beliebt Rechnen >

(1-x^2)y^{''}-2xy^'=1

Lösung

(1 - x^{2}) y^{^{''}} - 2 x y^{^{'}} = 1

Lösung

y = - \frac{1}{2} ln (1 - x^{2}) + c_{1} (\frac{ln ( x + 1 )}{2} - \frac{ln ( x - 1 )}{2}) + c_{2}

Schritte zur Lösung

(1 - x^{2}) y^{''} (x) - 2 x y^{'} (x) = 1

Solve using substitution:

y = - \frac{1}{2} ln (1 - x^{2}) + c_{1} (\frac{ln ( x + 1 )}{2} - \frac{ln ( x - 1 )}{2}) + c_{2}

y = - \frac{1}{2} ln (1 - x^{2}) + c_{1} (\frac{ln ( x + 1 )}{2} - \frac{ln ( x - 1 )}{2}) + c_{2}

Graph

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