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Beliebt Rechnen >

(dx)/(dt)=(x^2+tsqrt(9t^2+x^2))/(tx)

Lösung

\frac{d x}{d t} = \frac{x ^{2} + t 9 t ^{2} + x ^{2}}{t x}

Lösung

x = ln^{2} (t) + 2 c_{1} ln (t) + c_{1}^{2} - 9 t, x = - t ln^{2} (t) + 2 c_{1} ln (t) + c_{1}^{2} - 9

Schritte zur Lösung

\frac{d x}{d t} = \frac{x ^{2} + t 9 t ^{2} + x ^{2}}{t x}

Solve using substitution:

x = ln^{2} (t) + 2 c_{1} ln (t) + c_{1}^{2} - 9 t, x = - t ln^{2} (t) + 2 c_{1} ln (t) + c_{1}^{2} - 9

x = ln^{2} (t) + 2 c_{1} ln (t) + c_{1}^{2} - 9 t, x = - t ln^{2} (t) + 2 c_{1} ln (t) + c_{1}^{2} - 9

Graph

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