625y^{''''}=81y

Lösung

625 y^{^{''''}} = 81 y

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

Schritte zur Lösung

625 y^{(4)} (t) = 81 y

Solve linear ODE:

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

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

y^{^{''}} + 4 y = 0, y (0) = 2, y^{^{'}} (0) = - 1

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

y^{^{''}} - 225 y = 0

y^{^{''}} + y = 0, y^{^{'}} (π) = 1, y (0) = 0

2 x^{^{''}} + 10 x = 0