What is the solution for x^{''''}=0 ?

The solution for x^{''''}=0 is x=(c_{1}t^3)/6+(c_{2}t^2)/2+c_{3}t+c_{4}

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x^{''''}=0

x^{^{''''}} = 0

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

Solution steps

x^{(4)} (t) = 0

Solve

x^{(4)} (t) = 0 : x^{'''} (t) = c_{1}

Solve

x^{'''} (t) = c_{1} : x^{''} (t) = c_{1} t + c_{2}

Solve

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

Solve

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

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

x \to 5 lim (x)

y^{^{''}} - y^{^{'}} - 6 y = 0, y^{^{'}} (0) = - 6

\int \frac{2 - x}{x ^{2} - x + 1} d x

\int 6 e^{- 0.8 x} d x

n = 1 \sum \infty (\frac{π}{4})^{n}

What is the solution for x^{''''}=0 ?
The solution for x^{''''}=0 is x=(c_{1}t^3)/6+(c_{2}t^2)/2+c_{3}t+c_{4}