4(d^2x)/(dt^2)+c(dx)/(dt)+k(x)=0

Lösung

4 \frac{d ^{2} x}{d t ^{2}} + c \frac{d x}{d t} + k (x) = 0

x = c_{1} e^{\frac{t ( - c + c ^{2} - 16 k )}{8}} + c_{2} e^{\frac{t ( - c - c ^{2} - 16 k )}{8}}

Schritte zur Lösung

4 \frac{d ^{2} x}{d t ^{2}} + c \frac{d x}{d t} + k (x) = 0

Solve linear ODE:

x = c_{1} e^{\frac{t ( - c + c ^{2} - 16 k )}{8}} + c_{2} e^{\frac{t ( - c - c ^{2} - 16 k )}{8}}

x = c_{1} e^{\frac{t ( - c + c ^{2} - 16 k )}{8}} + c_{2} e^{\frac{t ( - c - c ^{2} - 16 k )}{8}}

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = - 4, y^{^{'}} (0) = 18

16 y^{^{''}} - 8 y + 145 y = 0, y (0) = - 2, y^{^{'}} (0) = 1

y^{^{'''}} - 3 y^{^{''}} - 13 y^{^{'}} + 15 y = 0

27 y^{^{''}} + (15 - 95) y^{^{'}} - 55 y = 0

324 y^{^{''}} - 612 y^{^{'}} + 289 y = 0, y (0) = 8, y^{^{'}} (0) = 5