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Beliebt Rechnen >

y^'=y^2-9

Lösung

y^{^{'}} = y^{2} - 9

Lösung

y = \frac{3 e ^{6 c_{1}}}{e ^{6 t} - e ^{6 c_{1}}} + \frac{3 e ^{6 t}}{e ^{6 t} - e ^{6 c_{1}}}

Schritte zur Lösung

y^{'} (t) = y^{2} - 9

Löse nach

t, y^{'} (t) = \frac{d y}{d t} = \frac{1}{\frac{d t}{d y}} = \frac{1}{t ^{^{'}}}

(\frac{1}{t ^{^{^{'}}}}) = y^{2} - 9

Isoliere

t^{^{'}} : t^{^{'}} = \frac{1}{y ^{2} - 9}

Wenn

f^{^{'}} (x) = g (x)

dann

f (x) = \int g (x) d x

t = \int \frac{1}{y ^{2} - 9} d y

\int \frac{1}{y ^{2} - 9} d y = - \frac{1}{6} (ln (\frac{y}{3} + 1) - ln (\frac{y}{3} - 1)) + c_{1}

t = - \frac{1}{6} (ln (\frac{y}{3} + 1) - ln (\frac{y}{3} - 1)) + c_{1}

Isoliere

y : y = \frac{3 e ^{6 c_{1}}}{e ^{6 t} - e ^{6 c_{1}}} + \frac{3 e ^{6 t}}{e ^{6 t} - e ^{6 c_{1}}}

y = \frac{3 e ^{6 c_{1}}}{e ^{6 t} - e ^{6 c_{1}}} + \frac{3 e ^{6 t}}{e ^{6 t} - e ^{6 c_{1}}}

Graph

Beliebte Beispiele

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