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

Lösung

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

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

Schritte zur Lösung

y^{(4)} (t) - 3 y^{'''} (t) + 3 y^{''} (t) = 0

Solve linear ODE:

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

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

y^{^{''''}} - 7 y^{^{'''}} + 18 y^{^{''}} - 20 y^{^{'}} + 8 y = 0

- y^{^{''}} - 2 \cdot π^{2} y = 0

y^{^{''}} + 64 y^{^{'}} + 16 y = 0

y^{^{''}} - 14 y^{^{'}} + 49 y = 0, y (0) = 0, y^{^{'}} (0) = 8

y^{^{''}} + 3 y^{^{'}} - 4 y = 0, y (0) = 0, y^{^{'}} (0) = 1