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

Lösung

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

y = c_{1} + c_{2} e^{- 33 t} + e^{\frac{3 3 t}{2}} (c_{3} cos (\frac{6 243 t}{2}) + c_{4} sin (\frac{6 243 t}{2}))

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- 33 t} + e^{\frac{3 3 t}{2}} (c_{3} cos (\frac{6 243 t}{2}) + c_{4} sin (\frac{6 243 t}{2}))

y = c_{1} + c_{2} e^{- 33 t} + e^{\frac{3 3 t}{2}} (c_{3} cos (\frac{6 243 t}{2}) + c_{4} sin (\frac{6 243 t}{2}))

\frac{y ^{^{''}}}{y ^{^{'}}} = a

9 y^{^{''}} + 12 y^{^{'}} + 4 y = 0, y (0) = - 3, y^{^{'}} (0) = 0

y^{^{''}} + 4 y = 0, y (0) = 0, y^{^{'}} (0) = \frac{12}{5}

y^{^{''}} - 24 y^{^{'}} + 12 y = 0

y^{^{''}} + 25 y = 0, y (0) = 4, y^{^{'}} (0) = - 2