(d^3x)/(dt^3)=4t^3+t

Lösung

\frac{d ^{3} x}{d t ^{3}} = 4 t^{3} + t

x = \frac{t ^{6}}{30} + \frac{t ^{4}}{24} + \frac{c _{1} t ^{2}}{2} + c_{2} t + c_{3}

Schritte zur Lösung

\frac{d ^{3} x}{d t ^{3}} = 4 t^{3} + t

Ersetze

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

mit

x^{'''} (t)

x^{^{'''}} (t) = 4 t^{3} + t

Löse

x^{'''} (t) = 4 t^{3} + t : x^{''} (t) = t^{4} + \frac{t ^{2}}{2} + c_{1}

Löse

x^{''} (t) = t^{4} + \frac{t ^{2}}{2} + c_{1} : x^{'} (t) = \frac{t ^{5}}{5} + \frac{t ^{3}}{6} + c_{1} t + c_{2}

Löse

x^{'} (t) = \frac{t ^{5}}{5} + \frac{t ^{3}}{6} + c_{1} t + c_{2} : x = \frac{t ^{6}}{30} + \frac{t ^{4}}{24} + \frac{c _{1} t ^{2}}{2} + c_{2} t + c_{3}

x = \frac{t ^{6}}{30} + \frac{t ^{4}}{24} + \frac{c _{1} t ^{2}}{2} + c_{2} t + c_{3}

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