solvefor x,(d^2x)/(dt^2)=2x^3

Lösung

löse nach

x, \frac{d ^{2} x}{d t ^{2}} = 2 x^{3}

x = 3 \frac{\frac{d ^{2} x}{d t ^{2}}}{2}, x = - \frac{3 \frac{\frac{d ^{2} x}{d t ^{2}}}{2}}{2} + \frac{3 \frac{\frac{d ^{2} x}{d t ^{2}}}{2} 3}{2} i, x = - \frac{3 \frac{\frac{d ^{2} x}{d t ^{2}}}{2}}{2} - \frac{3 \frac{\frac{d ^{2} x}{d t ^{2}}}{2} 3}{2} i

Schritte zur Lösung

\frac{d ^{2} x}{d t ^{2}} = 2 x^{3}

Tausche die Seiten

2 x^{3} = \frac{d ^{2} x}{d t ^{2}}

Teile beide Seiten durch

2

x^{3} = \frac{\frac{d ^{2} x}{d t ^{2}}}{2}

Für

x^{3} = f (a)

sind die Lösungen

x = 3 f (a), 3 f (a) \frac{- 1 - 3 i}{2}, 3 f (a) \frac{- 1 + 3 i}{2}

x = 3 \frac{\frac{d ^{2} x}{d t ^{2}}}{2}, x = 3 \frac{\frac{d ^{2} x}{d t ^{2}}}{2} \frac{- 1 + 3 i}{2}, x = 3 \frac{\frac{d ^{2} x}{d t ^{2}}}{2} \frac{- 1 - 3 i}{2}

Vereinfache

3 \frac{\frac{d ^{2} x}{d t ^{2}}}{2} \frac{- 1 + 3 i}{2} : - \frac{3 \frac{\frac{d ^{2} x}{d t ^{2}}}{2}}{2} + \frac{3 \frac{\frac{d ^{2} x}{d t ^{2}}}{2} 3}{2} i

Vereinfache

3 \frac{\frac{d ^{2} x}{d t ^{2}}}{2} \frac{- 1 - 3 i}{2} : - \frac{3 \frac{\frac{d ^{2} x}{d t ^{2}}}{2}}{2} - \frac{3 \frac{\frac{d ^{2} x}{d t ^{2}}}{2} 3}{2} i

x = 3 \frac{\frac{d ^{2} x}{d t ^{2}}}{2}, x = - \frac{3 \frac{\frac{d ^{2} x}{d t ^{2}}}{2}}{2} + \frac{3 \frac{\frac{d ^{2} x}{d t ^{2}}}{2} 3}{2} i, x = - \frac{3 \frac{\frac{d ^{2} x}{d t ^{2}}}{2}}{2} - \frac{3 \frac{\frac{d ^{2} x}{d t ^{2}}}{2} 3}{2} i

x^{4} + 11 x^{2} = 0

x^{3} - 13 x^{2} - x + 13 = 0

x^{4} + 7 x^{2} + 18 x + 10 = 0

roo t s x^{3} - 3 x^{2} + 2 x = 0

4 - 3.6 x + 3.6 x^{2} - 1.2 x^{3} = 0