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Beliebt Rechnen >

(d^2y)/(dx^2)y+81y=0

Lösung

\frac{d ^{2} y}{d x ^{2}} y + 81 y = 0

Lösung

y = - \frac{81 x ^{2}}{2} + c_{1} x + c_{2}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} y + 81 y = 0

Ersetze

\frac{d ^{2} y}{d x ^{2}}

mit

y^{''} (x)

y^{^{''}} (x) y + 81 y = 0

Isoliere

y^{''} (x) : y^{''} (x) = - 81

Löse

y^{''} (x) = - 81 : y^{'} (x) = - 81 x + c_{1}

Löse

y^{'} (x) = - 81 x + c_{1} : y = - \frac{81 x ^{2}}{2} + c_{1} x + c_{2}

y = - \frac{81 x ^{2}}{2} + c_{1} x + c_{2}

Graph

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