y^{(5)}+9y^'=0

Lösung

y^{(5)} + 9 y^{^{'}} = 0

y = c_{1} + e^{- \frac{3}{2} t} (c_{2} cos (\frac{3}{2} t) + c_{3} sin (\frac{3}{2} t)) + e^{\frac{3}{2} t} (c_{4} cos (\frac{3}{2} t) + c_{5} sin (\frac{3}{2} t))

Schritte zur Lösung

y^{(5)} + 9 y^{'} (t) = 0

Solve linear ODE:

y = c_{1} + e^{- \frac{3}{2} t} (c_{2} cos (\frac{3}{2} t) + c_{3} sin (\frac{3}{2} t)) + e^{\frac{3}{2} t} (c_{4} cos (\frac{3}{2} t) + c_{5} sin (\frac{3}{2} t))

y = c_{1} + e^{- \frac{3}{2} t} (c_{2} cos (\frac{3}{2} t) + c_{3} sin (\frac{3}{2} t)) + e^{\frac{3}{2} t} (c_{4} cos (\frac{3}{2} t) + c_{5} sin (\frac{3}{2} t))

(1 + e^{x}) y \cdot y^{^{'}} = e^{x}

\frac{d y}{d x} = \frac{10 ( 1 + x )}{x y}

\frac{d x}{d t} + cos (t) x = cos (t)

5 x y \frac{d y}{d x} = 4, y > 0

\frac{d v}{d t} = \frac{2}{9} v