y^{'''}+3y^{''}-30y^'-50y=0

Lösung

y^{^{'''}} + 3 y^{^{''}} - 30 y^{^{'}} - 50 y = 0

y = c_{1} e^{5 t} + c_{2} e^{(- 4 + 6) t} + c_{3} e^{(- 4 - 6) t}

Schritte zur Lösung

y^{'''} (t) + 3 y^{''} (t) - 30 y^{'} (t) - 50 y = 0

Solve linear ODE:

y = c_{1} e^{5 t} + c_{2} e^{(- 4 + 6) t} + c_{3} e^{(- 4 - 6) t}

y = c_{1} e^{5 t} + c_{2} e^{(- 4 + 6) t} + c_{3} e^{(- 4 - 6) t}

25 y^{^{''}} - 40 y^{^{'}} + 16 y = 0, y (0) = 4, y^{^{'}} (0) = - 3

y^{^{''}} - 16 y = 0, y (0) = 3, y^{^{'}} (0) = 5

\frac{d ^{4} y}{d x ^{4}} - \frac{d ^{2} y}{d x ^{2}} + 4 y = 0

\frac{d ^{2} y}{d x ^{2}} = 0.15 y, y (0) = 240, y (10) = 150

y^{^{''}} - 4 y^{^{'}} + 13 y = 0, y (0) = - 2, y^{^{'}} (0) = - 16