y^{''''}+y^{''}+9y=0

Lösung

y^{^{''''}} + y^{^{''}} + 9 y = 0

y = e^{\frac{5 t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2})) + e^{- \frac{5 t}{2}} (c_{3} cos (\frac{7 t}{2}) + c_{4} sin (\frac{7 t}{2}))

Schritte zur Lösung

y^{(4)} (t) + y^{''} (t) + 9 y = 0

Solve linear ODE:

y = e^{\frac{5 t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2})) + e^{- \frac{5 t}{2}} (c_{3} cos (\frac{7 t}{2}) + c_{4} sin (\frac{7 t}{2}))

y = e^{\frac{5 t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2})) + e^{- \frac{5 t}{2}} (c_{3} cos (\frac{7 t}{2}) + c_{4} sin (\frac{7 t}{2}))

y^{^{''}} - 7 y^{^{'}} + 10 y = 0, y (0) = 1, y^{^{'}} (0) = - 1

4 x^{^{''}} + 2 x = 0

y^{^{''}} - 10 y^{^{'}} - 98 y = 0

y^{^{''}} - 4 y^{^{'}} + y 5 = 0

y^{^{''}} - 9 y^{^{'}} + 7 y = 0